Query-driven Frequent Co-occurring Term Extraction over Relational Data using MapReduce

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by  Jianxin Li

Query-driven Frequent Co-occurring Term Extraction over
Relational Data using MapReduce
Jianxin Li Chengfei Liu Liang Yao
SwinburneUniversityof SwinburneUniversityof SwinburneUniversityof
Technology Technology Technology
Melbourne,Australia Melbourne,Australia Melbourne,Australia
[email protected] [email protected] [email protected]
Jeffrey Xu Yu Rui Zhou
3
1 ChineseUniversityofHong SwinburneUniversityof
0 Kong Technology
2 HongKong,China Melbourne,Australia
[email protected] [email protected]
n
a
J ABSTRACT SQLand MapReduce interfaces over avariety of storage mecha-

1 nisms. [3,4,5]summarizethestate-of-the-artscalabledataman-
In this paper we study how to efficiently compute frequent co-
1 agement systems for traditional and cloud computing infrastruc-
occurringterms(FCT)intheresultsofakeywordqueryinparallel
usingthepopularMapReduceframework. Takingasinputakey- tures.[3]highlightsupdateheavyandanalyticalworkloads.[4]in-
] troducessomeimportantapplicationexamplesforbigdatainreal
B wordqueryqandanintegerk, anFCTqueryreportsthekterms
life. [5] describessixdatamanagement research challenges rele-
D thatarenotinq,butappearmostfrequentlyintheresultsofthekey-
vantforbigdataandthecloud. Differently, inthispaperourtar-
wordqueryqovermultiplejoinedrelations.Thereturnedtermsof
. getistoaddresstheproblemofquery-drivenfrequentco-occurring
s FCTsearch can be used todo query expansion and query refine-
c mentfortraditionalkeywordsearch. Differentfromthemethodof termextractionoverbigdata,i.e.,computingthefrequentco-occurring
[ FCTsearchinasingleplatform, ourproposed approach caneffi- termsintheresultsofagivenkeywordquery.Thereturnedfrequent
cientlyansweraFCTqueryusingtheMapReduceParadigmwith- co-occurring terms, as the informative feedbacks, can be used to
1
refinetheoriginalkeywordquerybeforetheexactresultset ofthe
v outpre-computingtheresultsoftheoriginalkeywordquery,which
originalqueryisretrieved.
8 is run in parallel platform. In this work, we can output the final
Sincetraditionalkeywordsearchoftenassumesthatthedatasets
7 FCTsearchresultsbytwoMapReducejobs: thefirstistoextract
should be loaded and processed in memory, it is not suitable to
3 thestatisticalinformationofthedata;andthesecondistocalculate
dealwithkeywordsearchoverbigdata.Thechallengescomefrom
2 thetotalfrequencyofeachtermbasedontheoutputofthefirstjob.
three points: (1) the ambiguity of keyword query limits the ex-
. AtthetwoMapReducejobs,wewouldguaranteetheloadbalance
1 pressiveness of search intention and may lead to a large number
ofmappersandthecomputationalbalanceofreducersasmuch as
0 ofuninterestingresults,whichmaymaketheusersfrustratedeas-
possible. Analyticalandexperimentalevaluationsdemonstratethe
3 ily; (2) evaluating keyword query over big data requires scalable
efficiency andscalabilityof our proposed approach using TPC-H
1 computationalparadigmwhereaparallelplatformisdesirable;(3)
benchmarkdatasetswithdifferentsizes.
v: generally, only simple index can be built for big data in practice
i duetothehugespacecost. Duetotheabovechallenges,thereare
X 1. INTRODUCTION onlyafewworkstodiscusstheproblemofkeywordsearchoverbig
r Recently, analyzing and querying big data are attracting more data. [6]addressesscalablekeywordsearchonlargedatastreams
a by pruning the unqualified tuples in a scalable method based on
andmoreresearchattentions,whichcanprovidevaluableinforma-
selection/semi-join strategy [7]. [8] addresses scalable keyword
tion to company and personal customers. Forexample, [1] com-
searchoverrelationaldatabyreturningpartofresults,ratherthan
bines a time-oriented data processing system with a MapReduce
thewholesetofresults,withinthespecifiedshorttime.
framework,whichcanallowuserstoperformanalyticsusingtem-
By extracting frequent co-occurring terms of a given original
poral queries - thesequeries are succinct, scale-out-agnostic, and
keyword query, we can have two advantages naturally. On the
easytowrite.[2]presentsdataparallelalgorithmsforsophisticated
searchengineside,itismoreprofitabletoconstrainuserstoaspe-
statisticaltechniques, withafocusondensitymethods,whichen-
cific set of results by exploiting the frequent co-occurring terms
ables agiledesign and flexiblealgorithmdevelopment using both
of the issued keyword queries from big data if the users are also
interestedintheextractedterms,whichcansavelotsofcomputa-
tionalresources.Ontheuserside,theuserscaneasilydiscoverthe
conceptsthatarecloselyassociatedwiththegivenkeywordsetby
extractingthefrequentco-occurredtermsfromthebigdata,which
Permission tomake digital orhardcopies ofall orpartofthis workfor
personalorclassroomuseisgrantedwithoutfeeprovidedthatcopiesare ishelpfulfortheuserstoeasilyunderstandtheirinterestinginfor-
notmadeordistributedforprofitorcommercialadvantageandthatcopies mationinthebigdata.
bearthisnoticeandthefullcitationonthefirstpage.Tocopyotherwise,to However, extracting such Frequent Co-occurring Terms (FCT)
republish,topostonserversortoredistributetolists,requirespriorspecific of a given keyword query ischallenging today, as there isan in-
permissionand/orafee.
creasingtrendofapplicationsbeingexpectedtodealwithvastamounts
Copyright20XXACMX-XXXXX-XX-X/XX/XX...$15.00.
ofdatathatusuallydonotfitinthemainmemoryofonemachine, sk(cid:13)s(cid:13)(cid:13)aT(cid:13)(cid:13) (cid:13)pMa(cid:13)(cid:13)(cid:13) sk(cid:13)s(cid:13)(cid:13)aT(cid:13)(cid:13) (cid:13)e(cid:13)cu(cid:13)d(cid:13)e(cid:13)R(cid:13)(cid:13)
e.g.,theGoogleN-gramdataset[9]andtheGeneBankdataset[10] SFD(cid:13)(cid:13)(cid:13) e(cid:13)l(cid:13)f(cid:13)f(cid:13)uh(cid:13)S(cid:13)(cid:13) e(cid:13)g(cid:13)r(cid:13)eM(cid:13)(cid:13) SFD(cid:13)(cid:13)(cid:13)
thatcontains100millionrecordswiththetotalsizeof416GB.Ap- 1(cid:13) (cid:13)k(cid:13)s(cid:13)aT(cid:13) (cid:13) (cid:13)e(cid:13)c(cid:13)ud(cid:13)e(cid:13)R(cid:13)(cid:13)
1(cid:13) (cid:13)k(cid:13)s(cid:13)aT(cid:13) (cid:13) (cid:13)pM(cid:13)a(cid:13)(cid:13)
plications withsuch datasetsusually make use of clustersof ma-
chines and employ parallel algorithmsin order toefficientlydeal 2(cid:13) (cid:13)k(cid:13)s(cid:13)aT(cid:13) (cid:13) (cid:13)e(cid:13)c(cid:13)ud(cid:13)e(cid:13)R(cid:13)(cid:13)
withthisvastamountofdata. Fordata-intensiveapplications, the 2(cid:13) (cid:13)k(cid:13)s(cid:13)aT(cid:13) (cid:13) (cid:13)pM(cid:13)a(cid:13)(cid:13)
MapReduce[11]paradigmhasrecentlyreceivedalotofattention 3(cid:13) (cid:13)k(cid:13)s(cid:13)aT(cid:13) (cid:13) (cid:13)e(cid:13)c(cid:13)ud(cid:13)e(cid:13)R(cid:13)(cid:13)
for being a scalable parallel shared-nothing data-processing plat-
form.Theframeworkisabletoscaletothousandsofnodes.Inthis 3(cid:13) (cid:13)k(cid:13)s(cid:13)aT(cid:13) (cid:13) (cid:13)pM(cid:13)a(cid:13)(cid:13)
4(cid:13) (cid:13)k(cid:13)s(cid:13)aT(cid:13) (cid:13) (cid:13)e(cid:13)c(cid:13)ud(cid:13)e(cid:13)R(cid:13)(cid:13)
paper,weuseMapReduceastheparalleldata-processingparadigm
for extracting the frequent co-occurring terms with regards to a
givenkeywordqueryoverabigdata.
Figure1:OverviewofMapReduce
Weknowthateachkeywordsearchresultofakeywordqueryin
relationaldatabaseincludesasetoftupleswhichareretrievedfrom
a single relation or several joined relations, and contains all the
for the MapReduce paradigm include processing crawled docu-
givenkeywordsofthekeywordquery.Intuitively,givenakeyword
ments,Webrequestlogs,etc.Intheopensourcecommunity,Hadoop
query and a big data, we can first compute the large number of
[13] is a popular implementation of this paradigm. In MapRe-
keywordsearchresultsandthencalculatethetotalfrequenciesfor
duce,dataisinitiallypartitionedacrossthenodesofaclusterand
each term in the result set. At last, all the terms can be sorted
stored in a distributed file system (DFS). Data is represented as
by their frequencies and the top-k frequent terms can be found.
(key,value)pairs. Thecomputationisexpressedusingtwofunc-
But this straightforward solution may make the feedbacks of the
tions:
returned termsmeaningless tothe users because the highly time- map (k ,v ) list(k ,v );
1 1 2 2
consuming evaluation of keyword query overbig datamay delay reduce (k ,list(v )) → list(k ,v ).
2 2 3 3
thefeedbacksgreatly. Figure1showsthedataflow→inaMapReducecomputation.The
Toreducetheprocessingtime,weproposeanewFCTapproach, computation starts with amap phase in which the map functions
whichcanavoidtheprocedureofdirectkeywordqueryevaluation areappliedinparallelondifferentpartitionsoftheinputdata. The
usingtheideaofstaralgorithmin[12]. Furthermore,ournewap- (key,value)pairsoutputbyeachmapfunctionarehash-partitioned
proach canefficientlyexplore thestatisticalinformation frombig onthekey. Foreachpartitionthepairsaresortedbytheirkeyand
dataandcomputethefrequenciesoftheco-occurringtermsusing then sent across the clusterin ashuffle phase. At each receiving
MapReduce. node, all the received partitions are merged in a sorted order by
Themaincontributionsinthispaperaresummarizedasfollows. theirkey. Allthepairvaluesthatshareacertainkeyarepassedto
a single reduce call. The output of each reduce function iswrit-
weproposeanovelMapReduce-basedapproachtoefficiently
• ten to a distributed file in the DFS. Besides the map and reduce
compute thequery-driven frequent co-occurring termsover
functions, the framework also allows the user to provide a com-
bigdata.
binefunctionthatisexecutedonthesamenodesasmappersright
we propose two shuffling strategies to guarantee the load/ afterthemapfunctions havefinished. Thisfunction actsasa lo-
• computationalbalanceofmappersandreducersbyconsider- calreducer, operatingonthelocal (key,value)pairs. Thisfunc-
ingboththeuniformeddatadistributionandtheunevendata tion allows the user to decrease the amount of data sent through
distribution. the network. The signature of the combine function is: combine
(k ,list(v )) list(k ,list(v )). Finally, the framework also
2 2 2 2
→
weconductedextensiveperformancestudiestodemonstrate allowstheusertoprovideinitializationandtear-downfunctionfor
•
thescalabilityofourproposedapproachusingTPC-Hbench- eachMapReducefunctionandcustomizehashingandcomparison
markdataset. functionstobeusedwhenpartitioningandsortingthekeys. From
Figure1onecannoticethesimilaritybetweentheMapReduceap-
Theremainderofthispaperisorganizedasfollows.InSection2,
proach and query-processing techniques for parallel DBMS [14,
weintroducetheworkingprocedureofMapReduceframeworkand
15].
anoptimizedmultiwayjoininMapReduceinmoredetails.Wede-
finetheproblemofquery-drivenfrequenttermextraction(denoted 2.2 Lagrangean Multipliers based Multiway
asFCTsearch)inSection3.Section4firstlydiscussesthepartition JoinsinMapReduce
strategiesforuniformeddatadistributionandunevendatadistribu-
Tolearnhowtooptimizemap-keysforamultiwayjoinin[16],
tion. And it then presents the procedures of computing frequent
let us begin with a simple example: the cyclic join R(A,B) 1
co-occurring terms of a query using MapReduce step by step. It
S(B,C)1T(A,C). Supposethatthetargetnumberofmap-keys
lastlyprovesthecorrectnessandcompletenessoftheMapReduce-
isk. Thatis,weshallusekReduceprocessestojointuplesfrom
based FCTsearch. Weprovidetheimplementationalgorithms of
thethreerelations. Eachof thethreeattributes A,B, andC will
ourapproachinSection5.Section6presentstheperformancestud-
haveashareofthekey,whichwedenotea,b,andc,respectively.
ies. Finally,wediscussrelatedworkinSection7andconcludein
WeassumetherearehashfunctionsthatmapvaluesofattributeA
Section8.
toadifferentbuckets,valuesofBtobbuckets,andvaluesofCto
cbuckets.Weusehasthehashfunctionname,regardlessofwhich
2. PRELIMINARIES
attribute’svalueisbeinghashed.Notethatabc=k.
Consider tuples (x,y)in relation R. WhichReduce processes
2.1 MapReduce Framework
need to know about this tuple? Recall that each Reduce process
MapReduce[11]isapopularparadigmfordata-intensiveparal- is associated with a map-key (u,v,w), where u is a hash value
lel computation inshared-nothing clusters. Example applications intherange1toa,representingabucketintowhichA-valuesare
hashed. Similarly,v isabucketintherange1tobrepresentinga Definition4. (JoiningNetworkofTupleSets)Ajoiningnetwork
B-value, and w isabucket intherange 1to crepresenting a C- oftuplesetsJnisatreeoftuplesetswhereforeachpairofadjacent
value. Tuple (x,y) from R can only be useful to this reducer if tuplesetsRiKi,RjKj inJn,thereisanedge(Ri,Rj)inG.
h(x)=uandh(y)=v.However,itcouldbeusefultoanyreducer
that has these first two key components, regardless of the value Here,RiKi representsthesetoftuplesofrelationRiwhereeach
ocfdwiff.erWenetcroendculcuedrsecthoarrte(sxp,oyn)dimngusttobkeeyrevpalilcuaetsed(ha(nxd)s,ehn(tyt)o,wth)e, ttuhpelseectoonftatuinpsleaspoafrtrieallaqtiuoenryRkjeywwhoerrdeseeatcKhtiuwplheilceoRntjKaijnrseaprpeasertniatsl
where1 ≤ w ≤ c. Similarreasoningtellsusthatanytuple(y,z) querykeywordsetKj.
from S must be sent to the a different reducers corresponding to
map-keys(u,h(y),h(z)),for1 u a. Finally,atuple(x,z) Definition5. (Candidate Network) Given a keyword query, a
≤ ≤
from T is sent to the b different reducers corresponding to map- candidate network C isajoining networkof tuplesets, such that
keys(h(x),v,h(z)),for1 v b. thereisaninstance I ofthedatabasethathasaMTJNTM C
≤ ≤ ∈
Thisreplicationof tupleshasa communication cost associated andnotuplet M thatmapstoafreetuplesetF C contains
∈ ∈
withit.ThenumberoftuplespassedfromtheMapprocessestothe anykeywords.
Reduceprocessesisrc+sa+tbwherer,s,andtarethenumbers
As the example shown in [17], for a keyword query “Smith,
of tuples in relations R, S, and T, respectively. Therefore, The
Miller”, J =ORDERSSmith 1CUSTOMER{} 1ORDERS{} is
optimizationproblemistominimizetheoverallcost:
notacandidatenetworkeventhoughthereisaMTJNTthatbelongs
MinimizeF(x)=rc+sa+tbsubjecttoabc=k toJ becauseJ issubsumedbyORDERSSmith1CUSTOMER{}
1ORDERSMiller. Here,CUSTOMER{}andORDERS{}denote
wherea,b,andcarethenumbersofbucketsofrelations,andkis
freetuplesets.
thenumberofreducetasks.
Themethod ofLagrangean multipliersservesuswell. Thatis, Definition6. (Top-k FCT Retrieval of Keyword Query) Given
westartwiththeexpressionrc+sa+tb−λ(abc−k),andtake akeywordquery q,anumber Rmax,andanintegerk,afrequent
derivativeswithrespecttothethreevariables, a,b,andc, andset co-occurringterm(FCT)queryreturnsthektermswiththehighest
theresultingexpressionsequalto0. Theresultisthreeequations: frequencies among all terms that (1) are not in q and (2) in the
s = λbc => sa = λk; t = λac => tb = λk; r = λab resultsofthekeywordqueryqw.r.t.themaximalnumberRmaxof
=> rc = λk. If we multiply the left sides of the three equa- joinedrelations.
tions and set that equal to the product of the right sides, we get
rstk = λ3k3 (remembering that abc on the left equals k). We To the problem of FCT retrieval, a straightforward solution is
can now solve for λ = 3 rst/k2. From this, the first equation to first solve the corresponding keyword query, and then extract
sa = λkyieldsa = 3 kprt/s2. Similarly,thenexttwoequations the term frequencies. However, the solution would incur expen-
p sivecostbecauseitneedstocompletelyevaluateallthejoins-the
yieldb= 3 krs/t2andc= 3 kst/r2.Whenwesubstitutethese
p p minimumtotaljoinnetworks(MTJNTs)ofthecorrespondingkey-
values in the original expression to be optimized, rc+sa+tb,
word query. To reduce the computational cost, [12] proposes a
wegettheminimumamountofcommunicationbetweenMapand
Reduceprocesses:3√3krst. star method toefficientlycalculate the termfrequencies without
completejoinevaluation.Itfirstobtainsallthecandidatenetworks
(CNs)ofthekeywordquerybyusingtheCN-generationalgorithm
3. PROBLEM DEFINITION
in[17]. Andthenit computes thetermfrequencies foreachCN.
WeconsiderthatthedatabasehasntablesR1, R2, ...,Rn,re- Atlast,allthecomputedtermfrequenciesaresummarizedintothe
ferredtoastherawtables.Theirreferencingrelationshipsaresum- totaltermfrequencieswithregardstotheFCTqueryoverthe data
marizedinaschemagraph: tobesearched.
Let us use h to represent the number of CNs. And a CN can
Definition1. (Schema Graph) The schema graph is a directed
be regarded as an algebraic expression, which retrieves a set of
graph G such that (1) G has n vertices, corresponding to tables
rvReef1re,ter.ex..n,RcRinjng(,1arep≤srpimeicat6=irvyejklye≤,yainnnd)R,(2iif.)aGndhaosnlayniefdRgejfhraosmavfeorrteeixgnRkietyo MTrMesTTMuJJlNNtTinTTJgNsc.fTarWon(CmbeeNedxoejeup)ctl=pouuytiφtnMbgfyoTCrtJwNNanoTiyC((1C1N≤N≤saii)ti≤tt6=hoehdjs)eanw≤moheteehtri.temhTweehe.saeThttahiovseferteMoMfosTTraeJJy,NN,tnThToes(CNi)
Definition2. (JoiningNetworkofTuples)Ajoiningnetworkof keywordsearchresultsetcanbedefinedasfollows.
tuplesjn isatreeoftupleswhereforeachpairofadjacenttuples
ti,tj jn,whereti Ri,tj Rj,thereisanedge(Ri,Rj)in h
Gand∈(ti1tj)∈(Ri∈1Rj). ∈ KSResult(q)= [MTJNT(CNi). (1)
i=1
Definition3. (Keyword Query) Given akeyword query, itsre-
sult is the set of all possible joining networks of tuples that are Letfreq-CN(CNi,w)bethetotalnumberofoccurrencesforterm
both: (1) Total- every keyword iscontained inatleast onetuple winalltheMTJNTsofMTJNT(CNi),orformally:
ofrfotmhethjoeinjoininginngetnweotrwko;r(k2)anMdinstiimllahla-vweeactaontanlojtorienminogveneatnwyotrukpolef freq-CN(CNi,w)= X Count(T,w). (2)
∀T∈MTJNT(CNi)
tuples.
whereCount(T,w)isdefinedasthenumberofoccurrencesofw
As such, we can call such joining networks as Minimal Total inasingleMTJNTT. Thus,thetotalfrequencyfreq(q,w)canbe
JoiningNetworksofTuples(MTJNT)ofthekeywordsinkeyword calculatedas:
query. Each MTJNT is a result instance of keyword query. To
h
improvetheefficiencyofkeywordquery,wecangroupthetuples
ofeachrelationbasedontheircontainedquerykeywords. freq(q,w)=Xfreq-CN(CNi,w). (3)
i=1
Accordingtotheaboveequation,theFCTretrieval(freq(q,w)) thedataindimensionaltablesaredistributeduniformly,i.e.,oneof
can be efficiently answered by alternatively calculating the term 8processorsneedtoprocess1.25 1011 joiningoperationsmaxi-
∗
frequencies (freq-CN(CNi,w)) of each candidate network CNi. mally.Theprocessorscanbelabelledasfollows: 000 001 010 011
Specifically,freq-CN(CNi,w)canbecalculatedefficientlywhen 100 101 110 111
However,ifoneofthedimensionaltablecontainsskewedtuples,
CNi is a star candidate network where a vertex, called the root,
thensomeprocessorswillbecomemuchhotterwhiletherestmay
connectstoalltheothervertices,calledtheleaves.
beidle.Evenifwecanaddmorenodestoincreasethescalabilityof
Although the star method is much better than the straightfor-
thesystem,itdoesnotsolvetheskewproblembecauseallskewed
wardone,itisstillexpensivetocomputeFCTretrievalbecause(1)
tupleswillstillbesenttothehotprocessors. Followingtheabove
itneedstoscanthedatatwice: scanningdataformakingstatisti-
instance,ifonlythetuplesinthefirstpartitionofdimensionaltable
calinformationandscanningdataforcomputingthefrequenciesof
S appear inthefact table R, then thehalf processors withlabels
termsindata;(2)itisasingle-machinebasedapproach,bywhich
100,101,110,111 will be always idle. That is to say, each pro-
long-timeprocessingwillbeincurredwhenthedatatobeprocessed
cessor of 000,001,010,011 has to deal with 2.5 1011 joining
ismassive;(3)IfCNiisnotastarcandidatenetwork,ithastose- ∗
operationsmaximally. Thiscaseoftenhappensinstar-schemejoin
lectsomerelationstodojoinoperationsexactly, whichisusedto
operationsbecauseitisdifficulttoguaranteethatdatainallthedi-
makestar-conversion. Inthispaper,westudytheproblemofFCT
mensionaltablesareevendistributed. Toaddresstheunbalanceof
retrievalintheparallelenvironment, i.e.,MapReduceframework,
computation,intuitivelywecansplitthedataintomorebulks(small
whichcanimprovetheperformancegreatly. Inthefollowing sec-
partitions)thatcanbedistributedasevenlyaspossible. However,
tion,wemainlyfocusonthecomplexcomputationofFCTretrieval
itisnoteasytomanagetheschedulingofthebignumberofbulks,
forstarcandidatenetworks.Forthenon-starcandidatenetwork,we
particularlywhenthebulksizeissmall.
canevaluatesomerelationstobeselectedusingtherepartitionjoin
strategyinMapReduce,whichiseasytobeimplemented[18].
4.2 Uneven Distribution-based Shuffling
4. MAPREDUCE-BASED FCT SEARCH Strategy
Differentfromthestarmethod,weloadandprocessthedatain Therearelotsofworktoprocessdataskewinparalleljoinsin
parallelusingMapReduce.However,makingthechangeisnottriv- database systems. However, most of the existing work primarily
ialbecauseMapReduceisashared-nothingparalleldataprocessing focusonthejoinoftworelations(R1S).Althougtheirapproaches
paradigm,andtheperformanceoftheFCTsearchwoulddependon canbeappliedtothejoinofmultiplerelationsbyrepeatedopera-
whetherthestrategyofdatapartitionisgoodornot.ForeachCN , tions,thelong-processingtimewouldbecomechallengingtosome
i
wecangetitsrelevanttermfrequenciesbytwoMapReducejobs. extent. Specifically, in this work our main problem is to address
Inthissection,wefirstproposeouroptimaldatapartitionstrat- star-scheme join that consists of one fact table and more dimen-
egy, by which the data can be distributed over the process nodes sional tables. From the study on the fact table, we can observe
withtheminimalduplicationswhileitguaranteesthereisnocom- thatthejoinedattributesinafacttableoftencontainsomeskewed
municationcostamongtheprocessnodesintheperiodofevaluat- tuplesoveroneorseveraljoineddimensions. Forexample,anair-
ingtheFCTsearch. Andthen, wedescribetheprocedures ofthe linecanprovidethebookingservicetotravelagentsandpersonal
twoMapReducejobsforaggregatingthetotaltermfrequencies.At customers at the same time. Generally, a travel agent may book
last, we analyze the properties of MapReduce-based FCT search thousands of tickets per year, but a personal customer can book
approach. onlyafewticketsperyear. Ifwetreatthetwotypesofcustomers
equally,thentheprocessorsdealingwithtravelagentswouldbehot
4.1 Uniformed Distribution-based Shuffling andtherestprocessorsdealingwithpersonalcustomerswouldbe
Strategy cooling(mostoftime,theyareidle.) Theoutputofhotprocessors
willgreatlydecreasetheoverallperformanceofparalleljoin.
Forthestar-schemejoin,wecanstillutilizetheLagrangeanMul-
ConsiderafactrelationR(A,B,C)andtwodimensionalrelations
tipliersbasedJoinstrategytopartitionthedata.Forexample,given
asetofrelationshavingR(A,B,C)1S(A,E)1T(B,F)1P(C,G), S(A,E)andT(B,F).AssumeScanbesplittedintothreepartitions:
S ,S ,andS ,andTissplittedintofourpartitions:T ,T ,T and
thecostexpressioncouldbe 0 1 2 0 1 2
T .Assuch,wehave12reducetasksthatneedtobecomputed.We
3
r+sbc+tac+pab needtoanswer:howtodistributethe12reducetasksintothekre-
ducers(e.g.,k=9)? Weshouldberemindedthatsomereducetasks
andtheLagrangeanequationsare:
doesnot producejoinedresultsoronlygenerateafewduetothe
tac+pab=λk,sbc+pab=λk,sbc+tac=λk dataskew.Todothis,weproposeacostmodeltoevaluatethecom-
putationalcostofeachreducetask.Anyformulaforestimatingthe
wherek=abc.Aftermakingthepair-comparisons,wecangetthe costofajoincouldbeused. Here,wechosethesimpletechnique
transformed equations: s/a = t/b = p/c. Thus, theminimum- ofestimatingthat
cost solution hasshares foreachvariable proportional tothesize cij = Rij est+ Siest+ Tj est+ Rij 1Si1Tj est
ofthedimensiontableinwhichitappears.Thatistosay,themap- where|Rij|estis|an|estimat|eo|fthenu|mberofRtuple|smapped
keyspartitionthefacttableintok parts, andeachpartofthefact totheredu|cet|asklabelledasij, Siestisanestimateofthenumber
tablegetsequal-sizedpiecesofeachdimensiontablewithwhichit ofStuplesmappedtothereduc|eta|skslabelledasi?(thequestion
isjoined.Asaresult,wecanderivea= 3 ks2/tp,b= 3 kt2/sp markmeansthatallpossiblereducetaskswhoselabelstarts with
p p
andc= p3 kp2/st. i),|Tj|est isanestimateofthenumberofTtuplesmappedtothe
Forinstance,ifwehave9PCasprocessors,i.e. k=9,andeach reducetaskslabelledas?j(similarly,thequestionmarkmeansthat
dimensionaltablecontains10,000tuples,theneachdimensionalta- allpossible reduce taskswhoselabel ends withj), Rij 1 Si 1
blecanbesplittedinto2partitions,i.e.,S0,S1,T0,T1,P0,andP1. Tj est isanestimateofthenumberoftuplesinRij|1 Si 1 Tj.
Obviously,thefacttablewiththemaximalsizeof10,0003 (1012) We| compute this estimate of the size of Rij 1 Si 1 Tj by as-
canbeapproximatelydistributedintothe8processorsonly when sumping thatthejoinattributevalues ineach joindimension Rij
are uniformly distributed. Once this estimate for the cost of the samekeys,whichcancompressthedatatobesent,e.g.,thepairsof
joiningof thereduce tasksarecomputed, anytaskscheduling al- s ands canbeaggregatedinto(a ,′′...,k ,...,k ,...2′′)where
1 2 1 1 1
|
gorithm can be used to try to balance the computational cost of thesymbol isusedtoseperatetheaggregatedtextinformationand
|
reducers.Inthiswork,weadoptaheuristicmethodtoschedulethe the local frequency of the tuples (e.g., s and s ) with the same
1 2
reducetasks. Forexample,wehave5reducetaskswiththeiresti- join attributekey (e.g., a ); the rest two pairs can be aggregated
1
matedcoststobecomputedovertworeducers. Thentheywillbe into(a ,′′...,k ,w ,w ,w ,...,k ,w 2′′).Inthisprocedure,the
2 1 1 2 3 1 2
|
assignedasshowninFigure2. querykeywords (e.g., k )canbepruned directly, whichdoesnot
1
affectthefollowingcalculation. Butwekeepitintheexamplein
ordertomaketheaggregationtobeunderstoodeasily.
For the tuples in a fact relation, the map function extracts all
the join attributes as the composite key k , and the texts of the
08(cid:13)(cid:13) 07(cid:13)(cid:13) 04(cid:13)(cid:13) 02(cid:13)(cid:13) 51(cid:13)(cid:13) restattributesastheaggregatedvalue v . 2Similarly, thecombine
2
functioncanbeappliedtoaggregatethevaluesofthetupleshaving
the same set of join attributes in order to minimize the network
traffic between the map and reduce functions. For example, the
mapfunctioncanoutputakey-valuepair(a b c ,′′w ,w ,...′′)
1 2 2 1 2
| |
for the tuple r in Figure 3(e). Similarly, we can transform the
1
)(cid:13)51(cid:13)1(cid:13)(cid:13)((cid:13) (cid:13)1(cid:13) (cid:13)r(cid:13)e(cid:13)cu(cid:13)d(cid:13)e(cid:13)(cid:13)r(cid:13) )(cid:13)01(cid:13)1(cid:13)(cid:13)((cid:13) (cid:13)2(cid:13) (cid:13)r(cid:13)e(cid:13)cu(cid:13)d(cid:13)e(cid:13)(cid:13)r(cid:13) othertuplesintokey-valuepairs.
Subsequently,thereducefunctioncomputesthestatisticalinfor-
Figure2:ExampleofAssigningReduceTasks mationforeachfacttupleanditscorrespondingdimensiontuples.
Firstly, it pulls all the dimension tuples from the DFS files and
To efficiently estimate the cost, in this paper we employ Sim- countsthenumberoftuplessharingthesamejoinattributeforeach
ple Random Sample to choose the tuples from R, S and T. Al- dimensionrelation,whicharestoredinavector,denotedas num-
thoughtherearealsootherclassificsamplingstrategies,e.g.,Strat- array. Andthen, itdeals withthefact tuples oneby one at each
ifiedsamplingandSystemanticsampling,theymayintroducemore reducer.Foreachfacttuple,weneedtoprobethenum-arraysofits
workload.Thedetailedcomparisonofsamplingstrategiesisoutof corresponding dimension relationsforproducing thecardinalities
thescopeofthispaper. ofthejoinattributes, whicharestoredinvectors, denoted asvol-
Afterthereducetasksarevirtuallyplacedtothereducersinbal- arrays. Afterallthefacttuplesareprocessedatareducer,itgen-
ance, the master node will construct an allocation table to main- eratesonevol-arrayforeachdimensionrelationandonevol-array
taintheschedulingrelationshipsbetweenbulksandreducers. For forthefactrelation,whichcanbeusedtocomputethefrequencies
example, if the reduce tasks R and R are grouped into the oftermsco-occurredwiththequerykeywordsatMapReduce2nd.
00 01
samereducer(e.g.,#reducer=1)together,thenthereducerwith
#reducer =1willpullthetuplesetsR00 andR01 fromthecor- 4.3.2 AllocateDatatoReduceTasksEvenly
responding mappers. Atthesametime, italsopull thetuplesets
Tounderstandthereducefunction,weneedtoanswertwoques-
S ,T andT fromthecorrespondingmappers.
0 0 1 tions. Thefirstoneis: howcanweallocatethedatatothereduce
4.3 Computing the Statistical Information at tasks as even as possible? Let’s consider the discussion in Sec-
MapReduce1st tion4.1again.Ifeachdimensiontableissplittedintotwopartitions
tobeprocessedbyreducersinparallel,thenitwillproduce 23 re-
4.3.1 Brief Procedure of Computing Statistical In- ducetasksthatarelabelledas 000 001 010 011 . Apossible
100 101 110 111
formation
way istolabel thedistinct joinattributeswithdifferent numbers.
AtMapReduce1st, themapfunction getsasinputstheoriginal Andthen, ahash functioncan beusedtomake theshuffle ofthe
tuples. For each tuple in dimensional relations, the function ex- data. Forexample, therearefourdistinctattributesincolumnA.
tractsthejoinattributeasthekey k2, andthetextsof therestat- We can assign the numbers as a1 1, a2 2, a3 3, and
tributesasthevaluev2. Tominimizethenetworktrafficbetween a4 4.Ifwestillwanttosplitthed→ataintotw→opartition→s,thenthe
themapandreducefunctions,weuseacombinefunctiontoaggre- has→h functioncan bedesigned ash(ai) = getNum(ai)MOD2
gatethevalueswiththesamekeyoutputbythemapfunctioninto where getNum(ai)isused toget thenumber of theattribute ai
asinglevalue. Andanumberisappendedtotheaggregatedvalue in A column. Based on the hash function, we have h(a ) = 1,
1
asthelocalfrequencyofthejoinattributeappearinginthecurrent h(a )=0,h(a )=1,andh(a )=0respectively. Similarly,we
2 3 4
split. Ifthejoinattributeistheprimarykeyofthecorresponding candesignhashfunctionsforthejoinattributesincolumn B and
relation,thenthecombineprocesscanbeskipped. columnC.
ConsidertheexampleinFigure3. Tomaketheloadbalanced, Accordingtothedesigned hash function, wecandistributethe
we assume that each table is splitted into two subtables with the tuplesinthefact tableand dimensiontablesintodifferent reduce
equal size asmuch aspossible, e.g., for S{k1}, thefirst partition tasks. Forthekey-valuepair(a b c ,′′w ,w ,...′′)tobegener-
1 2 2 1 2
size is l|S{k1}|/2m = 4 while the second partition is |S{k1}|− 1at0e0d.bAyttthheetusapmleert1i,mitew,fiollrbtheealkleoy|c-avt|aelduteophaAir(saw1)ithhBa(b,2t)hheCy(wci2l)lb=e
l|S{k1}|/2m = 3. The map function can read the tuples s1, s2, distributedtothereducetaskswith100,101,110and1111,respec-
s ,s andgeneratethecorrespondingkey-valuepairsforthefirst tively. Thekey-value pairswithb willbedistributedtothecor-
3 4 2
partition inFigure3(b). For s , theoutput key-value pairis(a , respondingreducetaskswith000,001,100,and101,respectively.
1 1
′′...,k ,...′′).Fors ,thekey-valuepairis(a ,′′k ,...′′).Similarly, Thekey-valuepairswithc willbedistributedtothecorresponding
1 2 1 1 2
the rest two tuples generate key-value pairs taking a as the key reducetaskswith000,010,100,and110,respectively.Allthedata
2
and the corresponding texts as their values respectively. By the inFigure3areallocatedasshowninFigure4, inwhichweonly
combinefunction,wecanaggregatethekey-valuepairshavingthe listthekeysofthekey-valuepairs. Inpractice,boththekeysand
}(cid:13)1Sk(cid:13)(cid:13)(cid:13){(cid:13) DI(cid:13)(cid:13) A(cid:13) t(cid:13)xe(cid:13) (cid:13)t(cid:13)
}(cid:13)t(cid:13)xe(cid:13)(cid:13)t(cid:13) (cid:13),A(cid:13){(cid:13)(cid:13) s(cid:13) a(cid:13) k(cid:13) (cid:13),(cid:13).(cid:13).(cid:13)..(cid:13)(cid:13).(cid:13).(cid:13) (cid:13),(cid:13) DI(cid:13)(cid:13) B(cid:13) t(cid:13)xe(cid:13) (cid:13)t(cid:13)
1(cid:13) 1(cid:13) 1(cid:13)
s(cid:13)2(cid:13) a(cid:13)1(cid:13) .(cid:13).k(cid:13).(cid:13)1(cid:13)(cid:13),(cid:13) t1(cid:13)(cid:13) kb(cid:13)(cid:13)1 (cid:13)(cid:13),(cid:13).(cid:13).(cid:13).(cid:13) 2w(cid:13),(cid:13)(cid:13)w (cid:13)3(cid:13)(cid:13),(cid:13).(cid:13).4(cid:13)(cid:13).(cid:13)
f(cid:13) s(cid:13)3(cid:13) ka(cid:13) (cid:13)(cid:13)2,(cid:13)(cid:13).(cid:13).(cid:13).(cid:13) w (cid:13)1(cid:13)(cid:13),(cid:13)w (cid:13)1(cid:13)(cid:13),(cid:13)w (cid:13)2(cid:13)(cid:13),(cid:13) 3(cid:13) t2(cid:13)(cid:13) b(cid:13)1(cid:13) k(cid:13)2(cid:13),(cid:13)ww (cid:13)1(cid:13)(cid:13)(cid:13),(cid:13) .(cid:13)2.(cid:13)(cid:13),(cid:13).(cid:13)
}(cid:13)t(cid:13)xe(cid:13)(cid:13)t(cid:13) C(cid:13) ,(cid:13)B(cid:13) (cid:13),A(cid:13){(cid:13)(cid:13) R(cid:13) s(cid:13)4(cid:13) a(cid:13)2(cid:13)k(cid:13) (cid:13),(cid:13).(cid:13).(cid:13).(cid:13) w (cid:13)1(cid:13)(cid:13),(cid:13) 2(cid:13) t3(cid:13)(cid:13) b(cid:13)2(cid:13) k(cid:13) (cid:13),(cid:13).(cid:13).(cid:13).(cid:13) 2(cid:13)
s(cid:13)5(cid:13) a(cid:13)2(cid:13)k(cid:13) (cid:13),(cid:13).(cid:13).(cid:13).(cid:13) w (cid:13)1(cid:13)(cid:13),(cid:13) 3(cid:13) t4(cid:13)(cid:13) b(cid:13)3(cid:13)k(cid:13) (cid:13),(cid:13).(cid:13).(cid:13).(cid:13) w (cid:13)2(cid:13)(cid:13),(cid:13) 2(cid:13)
}(cid:13)2Tk(cid:13)(cid:13){(cid:13)(cid:13) }P(cid:13)3k(cid:13)(cid:13)(cid:13){(cid:13) s(cid:13)6(cid:13) a(cid:13)3(cid:13) .(cid:13).k(cid:13).(cid:13)1(cid:13)(cid:13),(cid:13) t5(cid:13)(cid:13) bk(cid:13)3(cid:13)(cid:13) (cid:13),(cid:13).(cid:13).(cid:13).(cid:13) w (cid:13)2(cid:13)(cid:13),(cid:13)w (cid:13)1(cid:13)(cid:13),(cid:13) 3(cid:13)
}(cid:13)t(cid:13)xe(cid:13)(cid:13)t(cid:13) (cid:13),B(cid:13){(cid:13)(cid:13) }(cid:13)t(cid:13)xe(cid:13)(cid:13)t(cid:13) (cid:13),C(cid:13){(cid:13)(cid:13) s(cid:13)7(cid:13) a(cid:13)4(cid:13)k(cid:13) (cid:13),(cid:13).(cid:13).(cid:13).(cid:13) w (cid:13)1(cid:13)(cid:13),(cid:13) 4(cid:13) t6(cid:13)(cid:13) b(cid:13)4(cid:13)k(cid:13) (cid:13),(cid:13).(cid:13).(cid:13).(cid:13) w (cid:13)2(cid:13)(cid:13),(cid:13) 3(cid:13)
(a) Star-CN (b) S{k1} (c) T{k2}
DI(cid:13)(cid:13) C(cid:13) t(cid:13)xe(cid:13) (cid:13)t(cid:13)
p(cid:13)1(cid:13) kc(cid:13)(cid:13)1 (cid:13)(cid:13),(cid:13).(cid:13).(cid:13).(cid:13) 3w(cid:13),(cid:13)(cid:13)w (cid:13)1(cid:13)(cid:13),(cid:13).(cid:13).1(cid:13)(cid:13).(cid:13) DI(cid:13)(cid:13) A(cid:13) B(cid:13) C(cid:13) t(cid:13)xe(cid:13) (cid:13)t(cid:13)
p(cid:13)2(cid:13) c(cid:13)1(cid:13) k(cid:13)3(cid:13),(cid:13)ww (cid:13)1(cid:13)(cid:13)(cid:13),(cid:13) .(cid:13)2.(cid:13)(cid:13),(cid:13).(cid:13) r(cid:13)1(cid:13) a(cid:13)1(cid:13) b(cid:13)2(cid:13) c(cid:13)2(cid:13) ww (cid:13)1(cid:13)(cid:13)(cid:13),(cid:13) .(cid:13)2.(cid:13)(cid:13),(cid:13).(cid:13)
p(cid:13)3(cid:13) ck(cid:13)2(cid:13)(cid:13) (cid:13),(cid:13).(cid:13).(cid:13).(cid:13) w (cid:13)3(cid:13)(cid:13),(cid:13)w (cid:13)2(cid:13)(cid:13),(cid:13) 4(cid:13) r(cid:13)2(cid:13) a(cid:13)1(cid:13) b(cid:13)4(cid:13) c(cid:13)1(cid:13) .(cid:13).(cid:13).(cid:13)
r(cid:13) a(cid:13) b(cid:13) c(cid:13) w (cid:13)(cid:13),(cid:13).(cid:13).(cid:13).(cid:13)
3(cid:13) 5(cid:13) 2(cid:13) 2(cid:13) 2(cid:13)
p(cid:13) ck(cid:13)(cid:13) (cid:13),(cid:13).(cid:13).(cid:13).(cid:13) w (cid:13)(cid:13),(cid:13)w (cid:13)(cid:13),(cid:13)
4(cid:13) 2(cid:13) 3(cid:13) 2(cid:13) 3(cid:13)
p(cid:13)5(cid:13) c(cid:13)3(cid:13) k(cid:13) (cid:13),(cid:13).(cid:13).(cid:13).(cid:13) 3(cid:13) r(cid:13)4(cid:13) a(cid:13)2(cid:13) b(cid:13)4(cid:13) ck(cid:13)1(cid:13)(cid:13) (cid:13),(cid:13).(cid:13).(cid:13).(cid:13) w (cid:13)3(cid:13)(cid:13),(cid:13)w (cid:13)2(cid:13)(cid:13),(cid:13) 3(cid:13)
p(cid:13) c(cid:13) k(cid:13) (cid:13),(cid:13).(cid:13).(cid:13).(cid:13) w (cid:13)(cid:13),(cid:13) r(cid:13) a(cid:13) b(cid:13) c(cid:13) w (cid:13)(cid:13),(cid:13).(cid:13).(cid:13).(cid:13)
6(cid:13) 3(cid:13) 3(cid:13) 3(cid:13) 5(cid:13) 4(cid:13) 3(cid:13) 1(cid:13) 3(cid:13)
(d) P{k3} (e) Rφ
Figure3:Arunningexampleforaquery k ,k ,k
1 2 3
{ }
valuesofthekey-valuepairswillbeallocatedtogether. cannot makeanycontributionforthefinalresultsbecauseno fact
tuplesappearinthesetasks.Therefore,theseunusefulreducetasks
canbedirectlyprunedwithoutfurthercomputation,whichcanim-
00(cid:13) 0(cid:13) (cid:13) 10(cid:13) 0(cid:13) (cid:13) 01(cid:13) 0(cid:13) (cid:13) 11(cid:13) 0(cid:13) (cid:13)
provetheperformancealot.
a(cid:13) a(cid:13) ab(cid:13)(cid:13)|(cid:13)c(cid:13)|(cid:13) a(cid:13) a(cid:13) ab(cid:13)(cid:13)|(cid:13)c(cid:13)|(cid:13)
2(cid:13) 4(cid:13) 2(cid:13) 4(cid:13) 1(cid:13) 2(cid:13) 4(cid:13) 4(cid:13) 3(cid:13) 1(cid:13)
b(cid:13) b(cid:13) a(cid:13) a(cid:13) b(cid:13) a(cid:13) a(cid:13) After pruning the unuseful reduce tasks, the first reducer only
2(cid:13) 4(cid:13) 2(cid:13) 4(cid:13) 3(cid:13) 2(cid:13) 4(cid:13)
c(cid:13) b(cid:13) b(cid:13) c(cid:13) b(cid:13) needtoprocessthereducetask(100)whilethesecondreducerhas
2(cid:13) 2(cid:13) 4(cid:13) 2(cid:13) 3(cid:13)
c(cid:13) c(cid:13) todealwiththethreereducetasks(001,011,101).Ifwedon’tcon-
1(cid:13) 1(cid:13)
00(cid:13) 1(cid:13) (cid:13) 10(cid:13) 1(cid:13) (cid:13) 01(cid:13) 1(cid:13) (cid:13) 11(cid:13) 1(cid:13) (cid:13) siderotherinformation,thenwecansaythatthecomputationover
ab(cid:13)1(cid:13)(cid:13)|(cid:13)c2(cid:13)(cid:13)|(cid:13) 2(cid:13) ab(cid:13)1(cid:13)(cid:13)|(cid:13)c4(cid:13)(cid:13)|(cid:13) 1(cid:13) a(cid:13)1(cid:13) a(cid:13)1(cid:13) thetworeducershavebeenbalancedasmuchaspossiblebecause
ab(cid:13)5(cid:13)(cid:13)|(cid:13)c2(cid:13)(cid:13)|(cid:13) 2(cid:13) a(cid:13)1(cid:13) b(cid:13)3(cid:13) b(cid:13)3(cid:13) thefirstreducerneedstoprocesstwofactkey-valuepairswhilethe
a(cid:13)1(cid:13) b(cid:13)2(cid:13) b(cid:13)4(cid:13) c(cid:13)2(cid:13) c(cid:13)2(cid:13) secondreducerdealswiththreefactkey-valuepairs. However, if
b(cid:13) b(cid:13) c(cid:13)
2(cid:13) 4(cid:13) 1(cid:13) wedoasimplesampleoverthereducetask(100),wecanfindthat
c(cid:13)
2(cid:13) a doesnotexistinthereducetask(100). Therefore,thefactkey-
5
value pair with key of a b c can be pruned. At this moment,
5 2 2
| |
Figure4:DemonstrationoftheDataAllocation wecanfindthattheworkloadratioofthetworeducersare 1 : 3.
Toaddressthedataskew,wecanusethecostmodelinSection4.2
toevaluatethecostofeachreducetaskandgroupthemasevenas
4.3.3 AllocateReduceTaskstoReducersEffectively possible. Inthiscase,wecanallocatethereducetasks(100,101)
to thefirst reducer and the reduce tasks (001, 011) to thesecond
The second question is: how can we allocate the reduce tasks
reducer.
to reducers effectively? The naive method is to activate one re-
ducerforeachreducetask. Butthismethodisofteninfeasiblein
realapplication.Thisisbecausewecangeneratedifferentnumbers
of virtual reduce tasksforthesame computational task whilethe
numberofavailablephysicalreducersislimited. Anotherpossible
4.3.4 DetailedProcedureofComputingStatisticalIn-
method isto allocate the reduce tasks ina round-robin way. For
formation
example, thereducetaskswiththelabels000, 010, 100, and110
canbecomputedatthefirstreducerwhiletheresttaskscanbecal- Whenthereducerspullalltherelevantdatafromthecorrespond-
culated at thesecond reducer. Although it intends toachieve the ingmappers,itistimetobuildthelocalvol-arraysforthedimen-
computationbalancewithoutconsiderationofdatainformation,it sion andfact relations. Forthereduce task (001), itgetsthe fol-
oftenleadstounbalance ofcomputation duetothedataskew. In lowingkey-valuepairs: (a b c ,′′...,k ,w ,w′′),(a ,′′...,k ,
addition, different reduce tasksmay havedifferent computational w ,w ,w ;...,k ,w 2′′2)|,(4a| 1,′′...,k 3,w′′2),(a3 ,′′...2,k ,w′′1),
workload. The reducers with the allocation of heavy workloads (b1,′′.2..,k3′′),(b 1,′′..2.,|k ,w′′)2and(c1,′′..3.,k ,4w ,w ,1...;k4 ,
2 2 4 2 3 1 3 1 1 3
willtakemoreprocessingtimewhiletheoneswiththelightwork- w ,w ,... 2′′). Firstly,wecanbuildthenum-arraysforthejoin
1 2
|
loadswilltakelessprocessingtime. Especiallyfortheexamplein attributesA,BandC,respectively.
Figure4,thereducetaskswiththelabels000, 010, 110, and111 Forthelocalnum-arrayofS{k1},wehave
attribute num text attribute volume text
a 3 ′′...,k ,w ,w ,w ;...,k ,w ; c 5 ′′...,k ,w ,w ,...;k ,w ,w ,...′′
2 1 1 2 3 1 2 1 3 1 1 3 1 2
...,k1,w3′′ Forthelocalvol-arrayofRφ,wehave
a4 1 ′′...,k1,w4′′ attribute volume text
Forthelocalnum-arrayofT{k2},wehave a b c 6 ′′...,k ,w ,w′′
attribute num text a2|b4|c1 4 ′′...,w3′′ 2 3
b 1 ′′...,k′′ Sim4i|la3rl|y,1wecangetthevol-ar3raysatthesecondreducerasfol-
2 2
b 1 ′′...,k ,w′′ lows.
4 2 3
Forthelocalnum-arrayofP{k3},wehave Forthelocalvol-arrayofS{k1},wehave
attribute num text attribute volume text
c1 2 ′′...,k3,w1,w1,...;k3,w1,w2,...′′ a1 4 ′′...,k1,...;k1,...;
Afterwebuildthenum-arraysforthelocalpartitions, weneed Forthelocalvol-arrayofT{k2},wehave
to process the fact key-value pairs one by one. Since the reduce attribute volume text
task(001)onlyincludes(a2|b4|c1,′′...,k3,w2,w3′′),thelocalvol- b2 4 ′′...,k2
arraysofthefactanddimensiontablescanbebuiltasfollows. b 4 ′′...,k ,w′′
4 2 3
Forthelocalvol-arrayofS{k1},wehave Forthelocalvol-arrayofP{k3},wehave
attribute volume text attribute volume text
a2 2 ′.′....,.k,1k,1w,w3′′1,w2,w3;...,k1,w2; cc12 22 ′′′′......,,kk33,,ww12,,ww14,;......,;kk33,,ww12,,ww23′′,...′′
Forthelocalvol-arrayofT{k2},wehave Forthelocalvol-arrayofRφ,wehave
attribute volume text attribute volume text
b4 6 ′′...,k2,w3′′ a1 b2c2 4 ′′w1,w2,...′′
Forthelocalvol-arrayofP{k3},wehave a |b |c 4 ′′...′′
1 4 1
| |
attribute volume text
c 3 ′′...,k ,w ,w ,...;k ,w ,w ,...′′
1 3 1 1 3 1 2
4.4 Computing theTerm Frequency
Forthelocalvol-arrayofRφ,wehave
atMapReduce2nd
attribute volume text
a b c 6 ′′...,k ,w ,w′′ At MapReduce2nd, we will output the final results - frequent
2| 4| 1 3 2 3
Similarly,wecanprocessthereducetasksof011,100,and101, co-occurrenceswiththegivenkeywordquerybyutilizingthesta-
respectively. Sincethedimensionkey-valuepairsareoftenneeded tisticalinformationinvol-arraysatMapReduce1st.
tobecopiedacrossdifferentreducetasksaccordingtoouradopted ThemapfunctiontakesasinputstheintermediateresultsofMap
scheduling strategy, the by-product of the strategy is to avoid to Reduce1st,i.e.,vol-arraysconsistingofthreeparts:{joinattribute,
re-pull the key-value pairs if they have been obtained by the re- volume, textinformation}. Foreachrecordinthe vol-arrays, we
ducers. By doing this, we can reduce the communication cost breakthetextinformationintotokensetbyusinganytokenization
andguaranteethecorrectnessoftheresults. Forexample, there- methodandfilterthestopwordsfromthegeneratedtokenset. For
ducetasks001and011wouldbeprocessedatthefirstreducerto- eachdistincttoken,wecangetitslocalfrequencybycountingthe
gether. Afterwedealwiththereducetask001, thedatainforma- timesofthetokenappearinginthefilteredtokenset.Andthen,we
tionofa ,a ,c arereadyatthisreducer.Forthereducetask011, generatethefrequencyofthetokenatthemapperbymultiplyingits
2 4 1
the reducer only needs to pull the necessary key-value pairs (b , localfrequencyandthevolumeoftherecord,whichcanbetakenas
3
′′...,k ,w ;...,k ,w ,w 2′′) and (a b c , ′′...,w′′). As such, thevaluev .Thetokenistakenasthekeyk .Atthereducerstage,
2 2 2 1 3| 4| 3| 1 3 2 2
only the local num-array of T{k2} of the reduce task 001 needs thereducefunctionstartstocomputethetotaltermfrequency.Fora
tobeupdatedbyaddingthekey-valuepairofb . Fortheupdated certainkey,thereducefunctionpullsallthecorrespondingrecords
3
localnum-arrayofT{k2},wehave withthekeyfromallthemappers.
attribute num text Let’stakethetermw1 asanexampletoshowtheprocedureof
b 1 ′′...,k′′ MapReducer2nd. Assume there are two available mappers: the
2 2
b 2 ′′...,k ,w ;...,k ,w ,w′′ firstmappertakesasinputstheoutput ofthefirstreduceratMap
b3 1 ′′...,k2,w2′′ 2 1 3 Reducer1standthesecondmappertakesasinputstheoutputofthe
Afterp4rocessingthefactke2y-v3aluepair(a b c ,′′...,w′′),we second reducer at MapReducer1st. For the first mapper, it scans
4| 3| 1 3 eachrecordinvol-arraysandgeneratesthekey-valuepairs taking
canupdatethelocalvol-arraysofthefactanddimensiontablesas
follows. termaskeyanditscardinalityasvalue. Fortherecord a2,itfirst
Forthelocalvol-arrayofS{k1},wehave computesthelocalfrequencyofw1as1;andthenitcalculatesthe
cardinality by multiplying the local frequency and the volume of
attribute volume text
a2 2 ′.′....,.k,k,1w,w′′1,w2,w3;...,k1,w2; (thwe1,re2c)o.rdA,tet.hge.,s1am∗e2tim=e,2t;hleasottlhyeritkoeuyt-pvuatlsueapkaeiyrs-voaflutehepateirrmass
a 4 ′′...,1k ,w3′′ intherecordcanbeoutput. Similarly,therecord b3 outputs(w1,
4 1 4 1 2 = 2) andtherecord c outputs(w , 3 5 = 15). Forthe
Forthelocalvol-arrayofT{k2},wehave ∗ 1 1 ∗
secondmapper,itoutputsthekey-valuepairs(w ,3 2=6)byc
1 1
attribute volume text ∗
and(w ,1 4=4)bya b c ,respectively.
b3 2 ′′...,k2,w2;...,k2,w1,w3 Atth1ere∗ducerstage,ea1c|h2r|e2ducergetsallthekey-valuepairsof
b4 6 ′′...,k2,w3′′ the keys to be allocated to the reducer and adds the cardinalities
Forthelocalvol-arrayofP{k3},wehave of each termas thetotal frequency of the term. For w , itstotal
1
frequencyis2+2+15+6+4=29.
4.5 Propertities ofMapReduce-based 5. IMPLEMENTATION OF MAPREDUCE-
FCT Search BASED FCTSEARCH
In the above sections, we have introduced the concepts of our
THEOREM 1. (AggregationEqualTransformation)Theaggre- MapReduce-based FCTsearchapproach. Nowwepresentitsim-
gationofthenum-arraysandthevol-arraystobebuiltoverinde-
plementation, which includes the functions Map(), Reduce() and
pendent reduce tasksisequal tothosetobebuiltovertheaggre- getPartition() of MapReduce1st and the brief description of Map
gateddatainformationoftheindependentreducetasks. Reduce2nd,respectively.
PROOF. Forthenum-arrays, ifakeyappearsinareducetask,
thenallthekey-value pairswiththesamekeymustappearinthe Algorithm1Map(key,arecord)atMapReduce1st
reducetask.Itsaysthatthelocalfrequency(num)ofthekeyshould
1: key =getJoinAttribute(key,therecord);
betheglobalfrequency(num)ofthekeyintheoriginalrelations. new
2: ifType(key )isidentifiedasadimensionkeythen
Inotherwords, thenumof akey inareduce taskcanbeused to new
3: indexPos = getJoinAttrPosition(Type(key ), joinAttr-
serveallthereducetasksthatcontainthekey. Therefore, theag- new
TypeSet[]);
gregationofthenum-arraysoverindependent reducetaskscanbe
4: for(i=1;i<=numDuplicates;i++)do
equivalentlytransformedtothatwefirstaggregatethedistinctkey-
5: cPartition=Integer.toX-naryString(i);
valuepairsoftheindependent reducetasksandthencompute the
6: cPartition.insertBefore(‘*’,indexPos);
num-arraysovertheaggregateddata.Becausetheequivalenttrans-
7: Value =getValue(key,therecord);
formationofnum-arraysholds,thevol-arrayscanalsobebuiltby new
8: Emit(pair(indexPos,key ),pair(cPartition,Value ));
alternativelyaccessingtheaggregated dataoftheindependent re- new new
9: endfor
ducetasks.
10: else
11: keyset=getJoinAttribute(key,therecord);
BasedontheequivalenttransformationinTheorem1,thestatis-
12: priority = getJoinAttrPosition(Type(key keyset),
ticalresultsofonereducetaskcanbeusedforanotherreducetaskif P ∈
joinAttrTypeSet[]);
bothreducetasksincludethesamekeys.Therefore,twocorollaries
13: key=keyset.toString(‘|’);
canbederivedasfollows.
14: Value =getValue(keyset,therecord);
new
COROLLARY 1. (IncrementalComputation)Thenum-arraysand 15: Emit(pair(priority,key),Valuenew);
thevol-arrayscanbeincrementallybuiltacrossreducetasks. 16: endif
COROLLARY 2. (DataFiltering)Thereducersonlyneedtopull InAlgorithm1,weshowtheproceduresinMap()atMapReduce1st.
thenecessarydatainformationthathavenotbeenseen.
Whenadimensiontupleisread,itfirstextractsasthenewkeythe
joinattributeandgeneratesasthevalueastringbycombiningthe
Sincethederivationsareeasytobeunderstood, wedonotpro-
contentsoftherestattributes.Andthen,ittagsthekeywithanum-
videtheirproofsinthispaper. Accordingtotheabovetwocorol-
berwhereweusethepositionofitscorrespondingattributecolumn
laries,wecanfurtherimprovetheperformanceofourapproachby
infactrelation. Bydoingthis, wecanguaranteeateachreducer,
Reducing the communication cost due to the avoidance of thedatabelongingtothesamedimensionrelationwillbecollected
• therepeateddatatobepulled; together. Anditalsotagsthevaluewiththepartitiontobecopied,
whichisusedtoimplementthemultiwayjoinbaseddatapartition,
Accelaratingthecomputationofreducersbecausethereduc- asshowninLine4-Line9. Forafacttuple,themapfunctiontags
•
erscanstarttoworkearlyfortheexistingdatathathavebeen thekeywiththesumofthepositionnumbersoftheircorresponding
ready; attributecolumnsinfactrelation,whichguaranteesthatallthefact
tuplesshouldarriveafterallthedimensiontuplesatareducer.Dif-
Avoidingthecomputationfromscratchbyincrementallymain-
• ferentfromprocessingthedimensiontuples,wedon’tneedtotag
tainingthecomputationalresultsofthereducetasksthathave
thevaluesbecauseeachfacttuplewillbesenttoonlyonepartition
beenprocessed.
asshowninLine11-Line15.
For adapting to the multiway join based data partition, Algo-
COROLLARY 3. (CorrectnessandCompleteness)MapReduce-
rithm2redesigns thefunction getPartition()ofHadoop. Accord-
basedFCTSearchcancomputethetermfrequenciesforakeyword
ingtothespecifiednumberofreducetasks,i.e.,numReduceTasks,
queryoverbigdatacorrectlyandcompletely.
Line 1 is used to calculate the number (denoted as numDimPar-
PROOF. Accordingtotheuniformeddistribution-basedshuffling tition) of partitionsforeach dimension relation using the derived
strategyinSection4.1orunevendistribution-basedshufflingstrat- equations,e.g.,a= 3 ks2/tp,b= 3 kt2/spandc= 3 kp2/st
egyinSection4.2,wecanseethatforeachfacttuple,itwillbesent inSection4.1. Ifthepkey-valuepaircpomesfromadimenpsionrela-
toonereducetask,i.e.,noduplicatesacrossdifferentreducetasks. tion,wecancomputethelocalpartitionnumber,withregardstothe
Andforthefactanddimensionpartitiondataateachreducetask, dimensionrelation,tobeallocatedbythekey,asshowninLine3.
they can be used tocompute the termfrequencies independently. And then, itwillbe used tocompute theglobal partitionnumber
Therefore,itguaranteesthelocalcorrectnessandcompletenessof bycombiningitwiththepartitionnumbersoftheotherdimension
MapReduce-based FCTSearchforthepartitiondatawithregards relations,asshowninLine4-Line5.Similarly,wecanprocessthe
tothereducetask. key-value pairscoming fromfactrelation. Differently, thekey is
BasedontheaggregationequaltransformationinTheorem1,we oftenacompositekeythatconsistsofmultiplesinglekeys. There-
canconcludetheglobalcorrectnessandcompletenessofMapReduce- fore,weneedtofirstcalculatethelocalpartitionnumberforeach
basedFCTSearchbecausetheaggregatedresultsofallthereduce singlekeyandthentransformthesetoflocalpartitionnumbersinto
tasks can be equally transformed to compute the results over the aglobalpartitionnumber,asshowninLine8-Line12.
aggregateddatapartitions(i.e.,theoriginaldata). Algorithm3canbedividedintothreestages.Atthefirststagein
Algorithm 2 getPartition(key, value, numReduceTasks) at Algorithm3Reduce(key,arecord)atMapReduce1st
MapReduce1st
1: {Comments:thedimensiontuplesarealwaysprocessedbefore
1: {Comments: computethenumbernumDimPartitionsofparti- facttuples};
tionsfordimensionrelationfromnumReduceTasks}; 2: ifkey.second()isidentifiedasadimensionkeythen
2: ifkey.second()doesnotcontain‘|’,i.e.,adimensiontuplethen 3: ifhashi .contains(key.first())then
value
3: numPartition = (key.second().hashCode() & Inte- 4: hashi (key.first())=hash (key.first())+1;
num num
ger.MAX_VALUE)%numDimPartitions; 5: else
4: cPartition=value.first().replace(‘*’,numPartition); 6: hashi (key.first())=value.second();
value
5: return cPartition.toDecimal()asthenumberofpartition; 7: hashi (key.first())=1;
num
6: else 8: endif
7: newastringstr=‘’; 9: else
8: keys[]=key.second().split(’|’); 10: {Comments: allthedimensiontuplesbelongingtothispar-
9: forinti=0;i<keys.length;i++do titionhavearrived};
10: str+= (keys[i].hashCode() & Integer.MAX_VALUE) % 11: keys=key.first().split(‘|’);
numDimPartitions; 12: num =hashi (keys[i]);
i num
11: endfor 13: ifanynumi=0then
12: return str.toDecimal()asthenumberofpartition; 14: hashf 6(key)=value;
value
13: endif 15: hashf (key)= num ;
16: hashivol(keys[i])Q+= i num ;
vol Qj6=i j
17: endif
Line2-Line8,itcalculatesthetotalnumberofdimensionrecords 18: endif
withthesamejoinattributeaskey.AtthesecondstageinLine11- 19: {Comments: generate inputs for the reducer at
Line17,itcalculatesthevolumeforeachfacttupleusing numi MapReduce2nd};
Q
andthetotalvolumesforeachjoinattributeusingQj6=inumj,re- 20: foreachitemxinhashfvolorhashivoldo
spectively. AtthethirdstageinLine20-Line24, itgeneratesthe 21: foreachwordwinhashfori (x)do
value
intermediateresultsthatwillbetakenastheinputsofthereducer 22: Emit(w,hashfori(x));
vol
atMapReduce2nd. Sincethetagofthefactkeysisalwayslarger 23: endfor
than that of the dimension keys, any dimension relation has the 24: endfor
higherprioritythanthefactrelation. Therefore,weguaranteethat
thethreestagescanbeprocessedinastablesequence.
Therestworkissimilartotheclassificexampleofwordcount seenat[19].
usingMapReduce.Wetakeastheinputstheintermediateresultsof
thereduceratMapReduce1st. Andwecalculatethetotalfrequen- t(cid:13)c(cid:13)e(cid:13)l(cid:13)eS(cid:13) (cid:13)
ciesofeachterm.Afterthat,themerge-sortoperationisappliedto s(cid:13)dr(cid:13)to(cid:13)(cid:13)wc(cid:13)y(cid:13)e(cid:13)e(cid:13)(cid:13)lk(cid:13)(cid:13)e(cid:13)S(cid:13) (cid:13) TRA(cid:13)P(cid:13)(cid:13)(cid:13) s(cid:13)dr(cid:13)o(cid:13)w(cid:13)y(cid:13)e(cid:13)k(cid:13) (cid:13) REMO(cid:13)T(cid:13)S(cid:13)(cid:13)U(cid:13)(cid:13)C(cid:13)(cid:13)
theoutputsofthereducersatMapReduce2nd. Assuch, thetop-k
frequentwordsortermswillbefound.
RE(cid:13)I(cid:13)L(cid:13)P(cid:13)P(cid:13)U(cid:13)S(cid:13)(cid:13) MET(cid:13)(cid:13)I(cid:13)E(cid:13)N(cid:13)I(cid:13)L(cid:13)(cid:13) SR(cid:13)ED(cid:13)RO(cid:13)(cid:13)(cid:13)(cid:13) RE(cid:13)I(cid:13)L(cid:13)P(cid:13)P(cid:13)U(cid:13)S(cid:13)(cid:13) MET(cid:13)(cid:13)I(cid:13)E(cid:13)N(cid:13)I(cid:13)L(cid:13)(cid:13) SR(cid:13)ED(cid:13)RO(cid:13)(cid:13)(cid:13)(cid:13)
6. EXPERIMENTS (a) Star-Type (b) Chain-Type
Inthissection,westudytheperformanceofourproposedMapReduce-
t(cid:13)c(cid:13)e(cid:13)l(cid:13)eS(cid:13) (cid:13)
basedFCTsearchapproach. Allexperimentswereperformedona TRA(cid:13)P(cid:13)(cid:13)(cid:13) s(cid:13)dr(cid:13)o(cid:13)w(cid:13)y(cid:13)e(cid:13)k(cid:13) (cid:13)
9-machine cluster running Hadoop 1.0.3 [13] at SwinCloud plat-
form1. OnemachineservedastheHeadNoderunningCentOS-5
Linuxwith500GBharddiskallocatedasDFSstorage. TheHead RE(cid:13)I(cid:13)L(cid:13)P(cid:13)P(cid:13)U(cid:13)S(cid:13)(cid:13) MET(cid:13)(cid:13)I(cid:13)E(cid:13)N(cid:13)I(cid:13)L(cid:13)(cid:13) SR(cid:13)ED(cid:13)RO(cid:13)(cid:13)(cid:13)(cid:13) REMO(cid:13)T(cid:13)S(cid:13)(cid:13)U(cid:13)(cid:13)C(cid:13)(cid:13)
Node also serves as the Name Node and JobTracker at the same
(c) Mix-Type
time. Whilethe other 8 machines as Worker Nodes are the gen-
eralPCwith1GBRAM,whichcanbeusedforMapandReduce
Figure5:DesignedQueryTypes
tasks. And each Worker Node is configured to run one map and
onereducetaskconcurrently.Thedistributedfilesystemblocksize
issetto64MB.OnlytheHeadNodetakestheroleofstoragenode To test the stability of our approach, we design three types of
fortheDFS.AllthemachinesareconnectedviaaGigabit-Ethernet keywordqueriesasshowninFigure5.Inordertoguaranteethere-
network. sultsetsofthegeneratedkeywordqueriesarenotempty,weadopt
the following steps to generate keyword queries and record their
6.1 SelectionofDatasetandKeywordQueries experimentalresults. Let’stakethetype inFigure5(a)asanex-
1
ample:
AsTPC-H[19]isthemostwidelyusedbigdatabenchmark in
MapReducestudy,e.g.,[20,21,22],wegenerateasetofdatasets
runthestructuredqueriesandoutputtheresultsasthreebags
withdifferentsizes.Inordertodemonstratetheperformanceofthe •
oftexts,e.g.,forstar-type,wehave: selectbag(p*),bag(s*),
multiway-join inMapReduce, wedirectly linkthePARTrelation
bag(o*) from part p, supplier s, lineitemli, orders owhere
andtheSUPPLIERrelationtotherelationLINEITEM,bywhich
p.partkey=li.partkey&s.suppkey=li.suppkey&o.orderkey
the relationLINEITEMistaken asthe fact relationwhile the re-
=li.orderkey;
lationsPART,SUPPLIERandORDERSareconsideredasthedi-
mensionrelations.Inaddition,TheoriginalTPC-HSchemacanbe choosethetermsfromdifferentbagsasthequerykeywords;
•
1hadoop.ict.swin.edu.au Foreachkeywordquerytype,wegenerate3batchesofkey-
•
wordquerieswhereeachbatchcontains10randomkeyword shuffle space usage approximately takes 10% of the dataset size.
queries. FromFigure11,wefindthattheshufflespaceusageapproximately
takes17%ofthedatasetsize. ThisisbecauseforChain-Typeand
In thefollowing study, the average performance of each batch of
Mix-Typequeries, theORDERSrelationcanbereducedbyjoin-
keyword queriesareusedtomakecomparison, e.g., Q ,Q , and
1 2 ingwiththeCUSTOMERrelation, whichcanreducethenumber
Q representthethreebatchesforType ;Q ,Q ,andQ represent
3 1 4 5 6 ofORDERStuplestoinvolveinthemultiway-joinofMapReduce.
the three batches for Type ; Q , Q , and Q represent the three
2 7 8 9 Particularly,forChain-Typequeries,itsmultiway-joinusestwoat-
batchesforType .
3 tributes as the composite key, e.g., suppkey and orderkey in Fig-
To illustrate the advantages of parallel platforms, we first run
ure5. Inthiscase,thenumberofcopiesforadimensiontuple is
theFCTsearchofthequerybatchQ over1GBdataset insingle
1 much smallerthan thatof Star-Typetakingthreeattributes asthe
machine platform. Although the single machine has 4GB RAM,
compositekey.
500GB hard disk and it does not need shuffle operations, it still
FromexperimentalresultsofQ over10GBdataset,wefindthat
consumesabout4.5minstocompletetheFCTsearchofQ ,which 1
1 theshufflespaceusagesofthe8reducersareunbalanced. Forhalf
ismuchexpensivethanthat(about1.83mins)ofourparallelplat-
ofthereducers,theirindividualshufflespacecostisapproximately
formconsistingof8workernodes.Therefore,thefollowingexper-
344MB,inwhichthenumberofreduceinputrecordsis10,843,452.
imentalstudiesareonlyfocusedontheevaluationofourapproach
While for the other four reducers, their individual shuffle space
intheparallelplatform.
costisapproximately 144MB, inwhichthenumberof reducein-
6.2 Response Time put records is 4, 070, 586. From the result analysis, we can get
thattheunbalancedshufflingoftenhappenswhenwedealwithbig
Figure6-Figure8providetheresponsetimeofFCTsearchwhen
data,whichmayaffectthetotalperformancegreatly. Thisisalso
we process theselected keyword queries over the TPC-Hdataset
thereasonthattheshufflingtimecosttakesthehighpercentageof
withdifferentsizes:1GB,5GB,10GBand20GB,respectively.For
thetimecostofreducestageatMapReduce.
processing thequerybatchesQ -Q , wefirstmergethetworela-
4 9
tionsCUSTOMERandORDERS,andthenrunthemultiway-based 6.4 VerifyingUnevenDistribution-basedShuf-
MapReducejoinbytakingtheLINEITEMasthefactrelation. fling Strategy
Fromtheexperimentalresults,wefindthatmostoftimeisspent
ontheMapReduce1st stage. Forexample,forthequerybatchQ ,
1
theMapReduce1ststageconsumes1.25minswhiletheMapReduce2nd 16(cid:13)
stagetakes0.6minsfor1GBdataset;thefirststageconsumes3.25 ns)(cid:13) 14(cid:13)
minswhilethesecondtakes0.8minsfor5GBdataset;thefirststage e (mi 1102(cid:13)(cid:13)
consumes 6.1 mins while the second takes 0.81 mins for 10GB m
Ti 8(cid:13)
dataset;thefirststageconsumes11.33minswhilethesecondtakes se 6(cid:13)
0.93minsfor20GBdataset;Forotherquerybatches,wecangetthe on 4(cid:13)
similarobservationsthatthefirststagetakesthehighpercentageof sp 2(cid:13)
e
thetotalresponsetime. Inaddition,fromtheexperimentalresults, R 0(cid:13)
we can find that map() in MapReduce1st stage takes about 0.33 Q1(cid:13) Q4(cid:13) Q5(cid:13)
mins to load a block withsize of 64MB and the loading balance Queries(cid:13)
canbeguaranteedbysplittingthedatasetintomultipleblocks. No-Adjust(cid:13) Adjust(cid:13)
Forinstance,considerQ ,5GBdatasetand8mappers,itissplit-
1
tedinto68maptasksandeachmapperapproximatelyload8num-
berofblocks.Assuch,themapstagemaytakeabout0.33*8=2.64 Figure12:ResponseTimeofProcessingUnevenDataDistribu-
mins to finish all mappers’ workloads. At the reduce stage, the tion
shuffle() takes high timecost than sort() and reduce(), e.g., shuf-
fling spends 1.91 minswhile sorting takes 0.1 mins and reduce()
takes0.43minsforonereducerinprocessing5GBdatasetusing8 3(cid:13)
reducers. Fortunately,theshufflingcanbeprocessedinparallelat B)(cid:13)
G 2.5(cid:13)
themapstage. Basedonthis, wecanfindthattheresponse time e ( 2(cid:13)
cmaonstbewmithinriemgaizreddsttootmheax5{G2B.64d,at1a.s9e1t}an+d08.1w+or0k.e4r3n=od3e.1s.7minsat Shuffl 1.5(cid:13)
Fromtheresultanalysis,wecangetthatthetotalresponsetime ce 1(cid:13)
u
constrainstothemaximalvalueofloadingtimeandtheshuffling d 0.5(cid:13)
e
time. Toreducetheloadingtime,wecanaddmoreworkernodes R 0(cid:13)
intothecluster.Toreducetheshufflingtime,wesendeachfacttu- Q1(cid:13) Q4(cid:13) Q5(cid:13)
pleintoonereducetaskandcopytherequireddimensiontuplesinto Queries(cid:13)
theircorrespondingreducetasksbasedonourproposedscheduling
No-Adjust(cid:13) Adjust(cid:13)
strategy, which can reduce the shuffling operation times because
generallyfactrelationismuchlargerthandimensionrelations.
Figure13:ReduceShuffleCostofProcessingUnevenDataDis-
6.3 Reduce Shuffle Size
tribution
Figure 9-Figure 11 show the reduce shuffle space usage when
we process theselected keyword queries over the TPC-Hdataset Inorder to verify theuneven distribution-based shuffling strat-
with different sizes: 1GB, 5GB, 10GB and 20GB, respectively. egy,wemodifythe10GBdatasetintoadatasetwithmuchhigher
FromFigure9,wefindthattheshufflespaceusageapproximately data skew by removing some tuples and repeatedly adding some
takes 20% of the dataset size. From Figure 10, we find that the othertuples. Tomakeatradeoff betweentheestimatedprecision