Randomization and Approximation Techniques in Computer Science: Second International Workshop, RANDOM’98 Barcelona, Spain, October 8–10, 1998 Proceedings

393 Pages·1998·9.88 MB·English

by  Alan M. Frieze (auth.)

Lecture Notes in Computer Science 1518
Editedby G.Goos,J. Hartmanisand J.van Leeuwen
3
Berlin
Heidelberg
NewYork
Barcelona
Budapest
HongKong
London
Milan
Paris
Singapore
Tokyo
Michael Luby Jose´ Rolim
Maria Serna (Eds.)
Randomization and
Approximation Techniques
in Computer Science
Second International Workshop, RANDOM’98
Barcelona, Spain, October 8-10, 1998
Proceedings
1 3
SeriesEditors
GerhardGoos,KarlsruheUniversity,Germany
JurisHartmanis,CornellUniversity,NY,USA
JanvanLeeuwen,UtrechtUniversity,TheNetherlands
VolumeEditors
MichaelLuby
InternationalComputerScienceInstitute
1947CenterStreet,Suite600,Berkeley,CA94704-1198,USA
E-mail:[email protected]
Jose´D.P.Rolim
UniversityofGeneva,ComputerScienceDepartment
24,rueGe´ne´ralDufour,CH-1211Geneva4,Switzerland
E-mail:[email protected]
MariaSerna
UniversityofBarcelona(UPC)
JordiGironaSalgado1-3,E-08034Barcelona,Spain
E-mail:[email protected]
Cataloging-in-Publicationdataappliedfor
DieDeutscheBibliothek-CIP-Einheitsaufnahme
Randomizationandapproximationtechniquesincomputer
science:secondinternationalworkshop,RANDOM’98,Barcelona,
Spain,October8-10,1998;proceedings/MichaelLuby...
(Hrsg.).-Berlin;Heidelberg;NewYork;Barcelona;Budapest;
HongKong;London;Milan;Paris;Singapore;Tokyo:Springer,
1998
(Lecturenotesincomputerscience;Vol.1518)
ISBN3-540-65142-X
CRSubjectClassification(1991):F.2,G.1.2,G.1.6,G.2,G.3,E.1,I.3.5
ISSN0302-9743
ISBN3-540-65142-X Springer-VerlagBerlinHeidelbergNewYork
Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis
concerned,specificallytherightsoftranslation,reprinting,re-useofillustrations,recitation,broadcasting,
reproductiononmicrofilmsorinanyotherway,andstorageindatabanks.Duplicationofthispublication
orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,
initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer-Verlag.Violationsare
liableforprosecutionundertheGermanCopyrightLaw.
(cid:1)c Springer-VerlagBerlinHeidelberg1998
PrintedinGermany
Typesetting:Camera-readybyauthor
SPIN10692778 06/3142–543210 Printedonacid-freepaper
Foreword
The Workshop on Randomization and Approximation Techniques in Computer
Science, Random’98, focuses on algorithmic and complexity aspects arising
inthedevelopmentofe(cid:14)cientrandomizedsolutionstocomputationallydi(cid:14)cult
problems.Itaims,inparticular,atfosteringthecooperationamongpractitioners
andtheoreticiansandamongalgorithmicandcomplexityresearchersinthe(cid:12)eld.
RANDOM’98, held at the University of Barcelona (UPC), October 8{10, 1998,
is the second in the series, after Bologna.
This volume contains all contributed papers accepted for presentation at
the workshop, together with invited lectures by Josep D(cid:19)(cid:16)az (UPC Barcelona),
Alan M. Frieze (Carnegie Mellon U.), Michael Luby (ICSI Berkeley), and Emo
Welzl (ETH Zu¨rich). The contributed papers were selected out of several dozen
submissions received in response to the call for papers. All papers published
in the workshop proceedings were selected by the program committee on the
basis of referee reports. Considerable e(cid:11)ort was devoted to the evaluation of the
submissionsbytheprogramcommitteeandanumberofotherreferees.Extensive
feedback was provided to authors as a result, which we hope has proven helpful
to them.
Wewouldliketothankalloftheauthorswhorespondedtothecallforpapers,
our invited speakers, the referees, and the members of the program committee:
Michael Luby, Chair, ICSI Berkeley
Andrei Broder, Digital Systems Research Center
Bernard Chazelle, Princeton U.
Andrea Clementi, U. of Rome
Anna Karlin, U. of Washington
Richard Karp, U. of Washington
Claire Kenyon, U. of Paris Sud
Michael Mitzenmacher, Digital Systems Research Center
Rajeev Motwani, Stanford U.
Prabhakar Raghavan, IBM
Maria Serna, UPC Barcelona
Alistair Sinclair, U. of California, Berkeley
Madhu Sudan, MIT
Avi Wigderson, Hebrew U.
Peter Winkler, Bell Labs
We gratefully acknowledge support from the European Association INTAS,
the Comissionat per a Universitats i Recerca { Generalitat de Catalunya, and
Universitat Polit(cid:18)ecnica de Catalunya. Finally, we would like to thank Helena
Martinez,CarmeAlvarez,ConradoMartinez,andJordiPetitiSilvestrefortheir
help in the preparation of the meeting.
August 1998 Michael Luby, Jos(cid:19)e D. P. Rolim, Maria J. Serna
Contents
Invited Paper
Disjoint Paths in Expander Graphs via Random Walks: A Short Survey 1
Alan M. Frieze
Regular Papers
A Derandomization Using Min-Wise Independent Permutations 15
Andrei Z. Broder, Moses Charikar and Michael Mitzenmacher
An Algorithmic Embedding of Graphs via Perfect Matchings 25
Vojtech R¨odl, Andrzej Rucin´ski and Michelle Wagner
Deterministic Hypergraph Coloring and Its Applications 35
Chi-Jen Lu
On the De-randomization of Space-Bounded Computations 47
Roy Armoni
Talagrand’s Inequality and Locality in Distributed Computing 60
Devdatt P. Dubhashi
On-Line Bin-Stretching 71
Yossi Azar and Oded Regev
CombinatorialLinear Programming:Geometry Can Help 82
Bernd Ga¨rtner
A Note on Bounding the Mixing Time by Linear Programming 97
Abraham Sharell
Robotic Exploration,Brownian Motion and Electrical Resistance 116
Israel A. Wagner, Michael Lindenbaum and Alfred M. Bruckstein
Fringe Analysis of Synchronized Parallel Algorithms on 2-3 Trees 131
Ricardo Baeza-Yates, Joaquim Gabarro´ and Xavier Messeguer
On Balls and Bins with Deletions 145
Richard Cole, Alan Frieze, Bruce M. Maggs, Michael Mitzenmacher
Andr´ea W. Richa, Ramesh K. Sitamaran and Eli Upfal
“Balls into Bins” — A Simple and Tight Analysis 159
Martin Raab and Angelika Steger
VIII Contents
Invi te d Pap e r
Tornado Codes: Practical Erasure Codes Based on Random
Irregular Graphs 171
Michael Luby
Regular Papers
Using Approximation Hardness to Achieve Dependable Computation 172
Mike Burmester, Yvo Desmedt and Yongge Wang
Complexity of Sequential Pattern Matching Algorithms 187
Mireille R´egnier and Wojciech Szpankowski
A Random Server Model for Private Information Retrieval 200
Yael Gertner, Shafi Goldwasser and Tal Malkin
Almost Optimal (on the average)Combinatorial Algorithms for
Boolean Matrix Product Witnesses, Computing the Diameter 218
C.P. Schnorr and C.R. Subramanian
Randomized Lower Bounds for Online Path Coloring 232
Stefano Leonardi and Andrea Vitaletti
ParallelRandom Search and Tabu Search for the Minimal Consistent
Subset Selection Problem 248
Vicente Cerver´on and Ariadna Fuertes
On Various Cooling Schedules for Simulated Annealing Applied to the
Job Shop Problem 260
K. Steinh¨ofel, A. Albrecht and C.K. Wong
A High Performance Approximate Algorithm for the Steiner Problem
in Graphs 280
Pere Guitart and Josep M. Basart
Invited Paper
Random Geometric Problems on [0,1]2 294
Josep D´ıaz, Jordi Petit and Maria Serna
Regular Papers
A Role of Constraint in Self-Organization 307
Carlos Domingo, Osamu Watanabe and Tadashi Yamazaki
Cont ent s I X
Constructive Bounds and Exact Expectations for the Random
AssignmentProblem319
Don Coppersmith and Gregory B. Sorkin
The “Burnside Process” Converges Slowly 331
Leslie Ann Goldberg and Mark Jerrum
QuicksortAgain Revisited 346
Charles Knessl and Wojciech Szpankowski
Sampling Methods Applied to Dense Instances of Non-Boolean
Optimization Problems 357
Gunnar Andersson and Lars Engebretsen
Second-Order Methods for Distributed Approximate Single- and
Multicommodity Flow 369
S. Muthukrishnan and Torsten Suel
Author Index 385
Disjoint Paths in Expander Graphs via Random
Walks: a Short Survey
AlanM.Frieze
(cid:3)
DepartmentofMathematicalSciences
Carnegie-MellonUniversity
Pittsburgh
PA15213
USA
tcarbtAs
There has been a significant amount of research lately on solving the edge
disjoint path and related problems on expander graphs. We review the random
walkapproachofBroder,FriezeandUpfal.
1 onticuodtrIn
Thebasicproblemdiscussed in thispaper can bedescribedasfollows: we are given
a graph and a set of disjoint pairs of vertices in . If possible, find
edge disGjoin=t p(aVth;Es ) that join Kto for . WVe call this the Edge
DisjointPathsproblPemi . We alsoasiay tbhiat iis= -1ouatbelr;2;::: ;Kif suchpathsexistforany
set of pairs. For arbitrary graphs, decGidingKwhether such paths exist is in for
fixed K– Robertson and Seymour [16], but is -complete if is part of thPe in-
put,bKeingoneofKarp’soriginalproblems. ThisNnPegativeresultcKanbecircumvented
for certain classes of graphs, see Frank [7]. In this paperwe will focusonxpandere
aphsgr . Therehavebeenessentially twobasesforapproachestothis problemin this
context:(i)randomwalksand(ii)multicommodityflows. Ouraimhereistoprovidea
summaryoftheresultsknowntousatpresenttogetherwithanoutlineofsomeoftheir
proofs. Weemphasisetherandomwalkapproach,see[11,12,13]formoredetailon
themulticommodityflowapproach.
rexadEpnsahGrp Forcertainboundeddegreeexpandergraphs,PelegandUpfal
[15]showedthatif isasufficientlystrongexpanderthen is -routableforsome
(cid:15)
small constant G that depends only on the expansioGn prnoperties of the input
graph.Furtherm(cid:15)o(cid:28)reth1e=r3eisapolynomialtimealgorithmforconstructingsuchpaths.
This result has now been substantially improved and there is only a small factor
(essentially )betweenupperandlowerboundsformaximumroutability.
logn
SupportedinpartbyNSFgrantCCR9530974.E-mail:ud.uem.hcta.mmodna@rnala .
(cid:3)
(cid:77)(cid:46)(cid:32)(cid:76)(cid:117)(cid:98)(cid:121)(cid:44)(cid:32)(cid:74)(cid:46)(cid:32)(cid:82)(cid:111)(cid:108)(cid:105)(cid:109)(cid:44)(cid:32)(cid:97)(cid:110)(cid:100)(cid:32)(cid:77)(cid:46)(cid:32)(cid:83)(cid:101)(cid:114)(cid:110)(cid:97)(cid:32)(cid:40)(cid:69)(cid:100)(cid:115)(cid:46)(cid:41)(cid:58)(cid:32)(cid:82)(cid:65)(cid:78)(cid:68)(cid:79)(cid:77)(cid:39)(cid:57)(cid:56)(cid:44)(cid:32)(cid:76)(cid:78)(cid:67)(cid:83)(cid:32)(cid:49)(cid:53)(cid:49)(cid:56)(cid:44)(cid:32)(cid:112)(cid:112)(cid:46)(cid:32)(cid:49)(cid:45)(cid:49)(cid:52)(cid:44)(cid:32)(cid:49)(cid:57)(cid:57)(cid:56)(cid:46)
(cid:32) (cid:83)(cid:112)(cid:114)(cid:105)(cid:110)(cid:103)(cid:101)(cid:114)(cid:45)(cid:86)(cid:101)(cid:114)(cid:108)(cid:97)(cid:103)(cid:32)(cid:66)(cid:101)(cid:114)(cid:108)(cid:105)(cid:110)(cid:32)(cid:72)(cid:101)(cid:105)(cid:100)(cid:101)(cid:108)(cid:98)(cid:101)(cid:114)(cid:103)(cid:32)(cid:49)(cid:57)(cid:57)(cid:56)
(cid:50) (cid:65)(cid:46)(cid:77)(cid:46)(cid:32)(cid:70)(cid:114)(cid:105)(cid:101)(cid:122)(cid:101)
Using randomwalks, Broder, Frieze and Upfal[2] improvedthe resultof [15] to
obtain the same result for where depends only on the expansion
(cid:20)
propertiesofthegraph. MoKrer=ecnen=t(llyo,gthne)y[3]impr(cid:20)ovedthisbyreplacing by
foranypositiveconstant , attheexpenseofrequestinggreaterexpan(cid:20)sionp2r+op(cid:15)-
erties of . More recent(cid:15)ly>st0ill, Leighton, Rao and Srinivasan [13], using the rival
multi-comGmodityflowtechnologyhaveimprovedonthisbyshowingthatthe canbe
replacedby . InSection4 wewill showhowtherandomwalksapproach(cid:15)can be
improvedtoog(iv1e)thesameresult,Theorem3.Itisratherinterestingthatthese,inmany
waysquitedifferent,approachesseemtoyieldroughlythesameresults. Wenotethat
bothapproachesyieldanon-constructiveproof[3],[12](viathelocallemma)thatina
sufficientlystrongexpander isachievable.
2
oadmRnsaGhrp RandoKmg=ra(cid:10)ph(ns=ar(elowgenll)k)nowntobeexcellentexpandersandso
itisperhapsnotsurprisingthattheyveryhighly“routable”. Broder,Frieze,Suenand
Upfal[4] andFriezeandZhao[9] (seeTheorems7,8)showthattheyare -routable
where iswithin aconstantfactorof asimplelowerbound,somethingtKhathasnot
yetbeeKnachievedforarbitraryexpandergraphs.
woLotgineosnCathPetsS Onewayofgeneralisingtheproblemistoboundthe
numberofpathsthatuseanyoneedge,theeedgestiocnong ,bysomevalue inplace
ofone.BoundsonthenumberofroutablepairsinthiscasearegiveninTheogrem5.
cyaiDnmmeolbrp Inthedynamicversionoftheproblemeachvertexreceivesan
infinitestreamofrequestsforpathsstartingatthatvertex.Thetimesbetweenrequests
arerandomandpathsareareonlyrequiredforacertaintime(untilthecommunication
terminates)andthenthepathisdeleted.Againeachedgeinthenetworkshouldnotbe
usedbymorethan pathsatonce.
The random waglk approach gives a simple and fully distributed solution for this
problem. In [3] (see Theorem 6) we show that if the injection to the network and
thedurationof connectionsarebothcontrolledby Poisson processesthenthereis an
algorithmwhichachievesasteadystateutilizationofthenetworkwhichissimilarto
theutilizationachievedinthecaitts casesituation,Theorem5.
aoxtmoiinrppA gloArmtih So far we have only considered the case where all
requestsforpathshaveto befilled. Ifthisis notpossiblethenonemightbesatisfied
withfillingasmanyrequestsaspossible. KleinbergandRubinfeld[10](seeTheorem
10)provethatacertaingreedystrategyprovideshasaworst-caseperformanceratioof
order .
ertexVDisjointathsP 1=(lognloglogn) Finally,thereistheproblemoffindingvertexdisjointpaths
betweenagivensetofpairsofvertices.Intheworst-caseonecannotdobetterthanthe
minimumdegreeofthegraph. Theinterestthereforemustbeongraphswithdegrees
whichgrowwiththesizeofthegraph.Inthiscontextrandomgraphs[5]haveoptimal
routingproperties,towithinaconstantfactor.
The structureof the paper is nowas follows: Section 3 discusses the problemof
splitting an expander, a basic requirementfor finding edge disjoint paths. Section 4
detailstheaforementionedresultsonexpandergraphsandoutlinessomeoftheproofs
for the random walk approach. Section 5 details the results on random graphs and
outlines the corresponding proofs. Section 6 describes the result of Kleinberg and
Rubinfeld.Afinalsectionprovidessomeopenproblems.