DTIC ADA459890: A Novel Power-Efficient Broadcast Routing Algorithm Exploiting Broadcast Efficiency

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A Novel Power-Efficient Broadcast Routing
Algorithm Exploiting Broadcast Efficiency
Intae Kang and Radha Poovendran
Department of Electrical Engineering, Box 352500
University of Washington, Seattle, WA 98195-2500
email: {kangit,radha}@ee.washington.edu
Abstract—It has been shown that the problem of finding a We hope to spur the development of better power-efficient al-
broadcastroutingtreewithminimumtotaltransmitpowerisNP- gorithmsbyanalyzingthisproblemfromadifferentperspective
hard. Hence, developing a heuristic power-efficient algorithm is
and providing more insights.
crucial.Theseminalworkinthisareaisthewell-knownBroadcast
The remainder of this paper is organized as follows. In the
Incremental Power (BIP) algorithm with a recent addition called
Embedded Wireless Multicast Advantage (EWMA) algorithm. In next section, we briefly define a network model and provide
thispaper,wepresentyetanothernovelpower-efficientalgorithm background. In Section III, we discuss previous representative
for broadcast routing tree construction called Greedy Perimeter work on the power-efficient broadcast routing problem. In
Broadcast Efficiency (GPBE) algorithm. We also compare the
Section IV, we present a detailed description of our new
performance of these algorithms.
algorithm. Section V summarizes our simulation results and
Section VI concludes this paper.
I. INTRODUCTION
II. BACKGROUNDANDNETWORKMODEL
The problem of constructing a broadcast routing tree with We denote a network as a weighted directed graph G =
minimum total transmit power has been shown to be NP- (N,A) with a set N of nodes and a set A of directed edges
hard [1], [2], [7], [8]. Therefore, it becomes more crucial to (links), A = {(i,j)}. For a directed edge (i,j) ∈ A, let π(j)
investigate good heuristics which can lead to power-efficient denote the parent node of node j (i.e., π(j)=i). Each node is
algorithms. The most well-known power-efficient algorithms labeledwithanodeID∈{1,2,...,|N|}.Themainobjectiveis
up to now include Broadcast Incremental Power (BIP) [1],
to construct a power-efficient (minimum total transmit power)
and Embedded Wireless Multicast Advantage (EWMA) [2]. In
broadcast routing tree rooted at the source node.
both algorithms, a major theme in designing a power-efficient
We assume that each node (host) is equipped with an
algorithm is to fully exploit the wireless broadcast advantage.
omnidirectional antenna. The transmission power required to
At each step of the BIP [1] and EWMA [2] algorithms, reachanodeatadistancedisproportionaltodα assumingthat
either minimum incremental power (required power to reach
the proportionality constant is 1 for notational simplicity and
additionalnode)ormaximumgain(reductionintransmitpower α is the path loss (attenuation) factor that satisfies 2≤α≤4.
of other nodes by increasing the transmit power of a node) is
To avoid the undue complication of notation, we also assume
used as a decision criteria to determine the transmit power of
the receiver sensitivity threshold as 1 (0 dB).
each node, respectively. Previous simulation results confirmed
Definition 1 (Pairwise and Node Transmit Power): Given a
that these are some of the good choices of decision metrics at spanning tree T, the required pairwise transmit power Pij to
each greedy decision process. maintain a link (i,j) ∈ T from node i to j is Pij = dαij
In this paper, we show that the broadcast efficiency can be wheredij isthedistancebetween thenode iandj.The(node)
another good choice of a greedy decision metric. The basic transmit power assigned to node i by a routing algorithm is
idea is as follows: over a whole deployed region, the wireless
broadcastadvantageisthemostbeneficialinasubregionwhere PTX(i)=max{Pij}, for i=1,...,N (1)
j∈(cid:2)i
nodes are most densely deployed, because more nodes can
be simultaneously reached with the same amount of transmit where (cid:3)i is a set of adjacent (child) nodes of node i in the
tree.
power.
Unlike conventional wired networks, there is no perma-
The purpose of this paper is three-fold: (i) We first present
nent connection between the nodes in wireless networks. The
thatthebroadcastefficiencyisanotherviablemetricofagreedy
decision process. (ii) To demonstrate this, we provide a novel transmit power level {PTX(i)} assigned to each node i (and
node mobility, if it is a mobile adhoc network) determines the
power-efficientalgorithmutilizingthebroadcastefficiency.(iii)
network topology.
Definition 2 (Physical and Logical Neighbor): Ifanodeiis
This work was supported in part by NSF grant ANI-0093187, and ARO
grantDAAD19-02-1-0242. transmitting with power PTX(i), then the physical neighbor
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A Novel Power-Efficient Broadcast Routing Algorithm Exploiting
5b. GRANT NUMBER
Broadcast Efficiency
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Standard Form 298 (Rev. 8-98)
Prescribed by ANSI Std Z39-18
ℵi ={k | 0<Pik ≤PTX(i)}ofnodeiinawirelessnetwork as inner postsweeping, because the transmission range of a
is a set of all the nodes within the communication boundary. node is only allowed to shrink. Inner postsweeping can also
The logical neighbor (cid:3)i =adj(i)={k | π(k)=i} of node i be considered as an operation which makes a routing tree
is a set of adjacent nodes in a routing tree. consistent, meaning the difference between the physical and
In general, the physical neighbor determined by a network logical neighbor is small.
topology and (node) transmit power does not coincide with the
logical neighbor determined by a routing algorithm. Note that
B. Embedded Wireless Multicast Advantage (EWMA) Algo-
ℵj =∅ when PTX(j)=0 and (cid:3)i ⊆ℵi. rithm
Assuming dik > dij, the incremental power ∆Pjik of node
i is defined as the additional power required to reach another The novel technique EWMA presented in [2] can also be
node k [1], i.e., ∆Pjik =Pik−Pij. If we label every node in considered as a postsweeping but the fundamental difference
ℵi as ik in an increasing order of distance from node i (i.e., from the inner postsweeping is that the EWMA increases the
itra=nsim0,iti1p,o.w..e,ri|PℵiT|Xsu(ci)hothfantoPdieipi<caPniibqeifreppr<eseqn)t,edtheans tthhee t(rgaaninsm) iitnptoowtaelrtorafnesamchitnpoodweetroicshpeocksswibhlee.thHeernfucert,hwererewdiullctcioalnl
this operation as outer postsweeping. Note that EWMA can
sum of incremental power
be refined as EWMA = (MST) + (inner postsweep) +
|ℵ(cid:1)i|−1 (outer postsweep).1 The outer postsweep procedure is a
PTX(i)= ∆Piikik+1. monotonic non-increasing function of a input tree: if there is
k=0 gain,itchangesthetreestructuretoaccommodateit;otherwise,
GivenaspanningtreeT withnodeitransmittingwithpower it leaves the tree intact.
PTX(i), the total transmit power of this tree is Note that depending on the input to outer postsweep proce-
dure,theoutcomewillbedifferentingeneral.However,choos-
(cid:1) (cid:1)|ℵ(cid:1)i|−1
PTX(T)= PTX(i)= ∆Piii . (2) ing (MST)+(inner postsweep) as an initial starting point
k k+1 in [2] seems to be “natural” to achieve the most gain. In [5],
i∈N i∈N k=0
we presented an extensive comparison study of known power-
We denote a tree with minimum total transmit power as
efficientalgorithmswithvariousperformancemeasures,oneof
(cid:1)
T◦ = argmin PTX(T)= argmin PTX(i) (3) whichincludestheratioofleafnodes.BecauseMSThassmall
T⊂G(N,A) T⊂G(N,A) ratio of leaf nodes (see Fig. 1), relatively high proportion of
i∈N
(cid:1)|ℵ(cid:1)i|−1 nodes (source and relay nodes) actively transmits with smaller
= argmin ∆Pi . (4) power. This provides more search space to EWMA algorithm
i i
T⊂G(N,A) k k+1 to test for gains at an added computational complexity.
i∈N k=0
III. RELATEDWORK Mean Ratio of Leaf Nodes
100
Inthissection,webrieflydiscusstheunderlyingmechanisms
of previous works leading to power-efficiency in broadcast 80
routing. MST
% BIP
A. Broadcast Incremental Power (BIP) Algorithm Percentage 4600 MBEIWSPTMSSWAW
As noted earlier in (2), the total transmit power is the
20
same as the total incremental power. The BIP algorithm [1]
effectively solves the constrained optimization problem (4) to
0
find a solution to (3), where the constraint implicitly comes 0 50 100 150 200 250 300
Network Size
fromthefactthatallinnernodes(ij forj <k)mustbealways
included if an outer node ik is included. Fig.1. Comparisonofratioofleafnodes.
Otherheuristicswhichfurtherreducethetotaltransmitpower
after a routing tree is constructed were presented in [1]–[4]
as postsweep [1] or perNodeMinimalize procedure [3]. An IV. GPBEALGORITHMDESCRIPTION
important characteristic of postsweep procedure [1] is that, In this section, we introduce another decision metric which
while it is possible to reduce the transmit power of nodes, it captures the notion of wireless broadcast advantage well.
is not allowed to increase. Suppose a node j and its logical Definition 3 (Broadcast Efficiency): Let C denote a set
neighbor (cid:3)j (determined by a routing algorithm) lies within a nodes currently covered by the transmission range of other
transmission boundary of node i, i.e., {j}∪(cid:3)j ⊂ℵi. Because nodes. The number of newly covered nodes by node i, trans-
all child nodes of j can be reached by node i, the transmission mittingwithpowerPTX(i),is|ℵi\C|.Thewirelessbroadcast
from node j is redundant and hence can be eliminated giving
the savings of PTX(j). We will call this class of algorithms 1MSTdenotestheminimumweightspanningtree.
efficiency βi is defined as the number of newly covered nodes π4|dN2|
reached per unit transmit power E{β1(r)}
βi = P|ℵTiX\C(i|) for i∈N. (5) 2(cid:1) 1(cid:2)+(cid:1)(cid:2)(cid:2) 2(cid:1) π|N| E{β2(r)}
16d2
(cid:2)
When we need to emphasize that an edge (i,j) is established,
(cid:3) √ √
i.e., node i transmits to node j with transmit power PTX(i)= 2 2(cid:1) 0 d 2d 2d 2 2d 4d
Pij, we will use the notation (a) (b)
|ℵ \C| Fig.2. (a)Dependenceofbroadcastefficiencyonnodelocation(b)Compar-
βij = Pi for i,j ∈N,i(cid:9)=j. (6) isonofaveragebroadcastefficiencyonnode1and2.
ij
Note that assuming α = 2 and transmission range of node i
Although only two extreme cases are compared, it is intu-
is r, the broadcast efficiency is essentially the same as a node
itively clear that the node located at the center has the largest
density (up to a scale factor).
average broadcast efficiency. As a node moves away from
the center, the broadcast efficiency is monotonic decreasing
A. Location Dependence of Broadcast Efficiency functionofadistancefromthecenterlocation.FromFig.2(b),
Let’s examine how broadcast efficiency is dependent on the wecanobservethattheaveragebroadcastefficiencyislocation
location of a node. Assume that |N| nodes are randomly dis- dependent and the center of symmetric deploy region is the
tributedwiththefollowinguniformprobabilitydensityfunction optimal place where the broadcast efficiency can be proba-
(pdf) fXY(x,y) = |N|/(2d)2 over 0 ≤ x,y ≤ 2d region as bilistically best utilized.
showninFig.2(a).2Then,theaveragenumberofcoverednodes
E{|ℵi(r)|} as a function of transmission range r becomes B. Effect of Broadcast Efficiency on Routing Decision
E{|ℵi(r)|}=A·|N|/(2d)2 (7) Before we proceed further to detailed algorithm description,
weexamineafewexampleshowroutingdecisionscanbemade
where A is the area of intersection between the square deploy using broadcast efficiency as a decision criterion.
regionandthecircleofradiusr centeredatnodei.Comparing Example 1 (Colinear topology): Considerasimpletopology
the two nodes, one located at the center (node 1) and the where all nodes lie within a line segment. Node 1 tries
other located at the corner (node 2), we can intuitively infer to broadcast to other nodes. It was shown in [9] that the
that node 1 has 4 times the expected broadcast efficiency than transmission range assignment shown in the Fig. 3(a) is the
node 2 at the corner. This is because, on average, 4 times the optimal strategy in terms of total transmit power, which can
number of nodes can be simultaneously covered with the same be proved with Jensen’s inequality. The decision by the node 1
transmit power from node 1. Considering the boundary effect is as follows: The broadcast efficiency is β12 = 1/d2,β13 =
of deployed region, the exact form of the average broadcast 2/(2d)2,...,β15 = 4/(4d)2. In general, when there are |N|
efficiency of node 2 can be expressed as a function of radius r colinear nodes, the broadcast efficiency becomes
as follows: k−1 1
 πr2/4|N| = π|N| if r ≤2d β1k = ((k−1)d)2 = (k−1)d2 for k ≥2. (10)
r2 4d2 16d2 √
E{β2(r)}= 14π(2rd2)2+I14|Nd2| if 2d<√r ≤2 2d (8) Because β1k monotonically decreases as k gets larger, β12 is
4d2|N| = |N| if r >2 2d maximum. Hence, node 1 picks node 2 as a destination node.
r2 4d2 r2
By repeatedly applying this greedy decision algorithm to other
(cid:6) (cid:6)
r π/2−cos−1(2d/ρ) nodes, the routing tree shown in Fig. 3(a) can be constructed,
where I1 = ρ dθdρ which is also optimal.
2d cos−1(2d/ρ)
√
and α = 2 is used. For 2d < r ≤ 2 2d case, E{β2(r)} can
be simplified as
πd2+(cid:7)r (cid:8)π/2−cos−1(2d/ρ)(cid:9)ρ dρ|N| (cid:1) (cid:1) (cid:1) (cid:1) 1 4
E{β2(r)}=(cid:10) 2d (cid:11) r(cid:12)2 (cid:14)4d2 (9) 1 2 3 4 5 3 2 5
(cid:13)
1 2d 2d |N|
= π−cos−1 + r2−4d2 .
4 r r2 4d2 (a) (b)
By repeating the same analysis for node 1, we can get the Fig.3. (a)Routingdecisionforacolineartopology.(b)Routingdecisionat
curves shown in Fig. 2(b). Note that node 1 has consistently aboundary.
higher average broadcast efficiency.
Example 2 (General boundary behavior): Now let’s look at
2Wecansimilarlyrepeatthesameanalysisforacirculurtopology. another example shown in Fig. 3(b). At the first iteration,
suppose node 1 is transmitting with power dα and node 5 GPBE, EWMA, Total Power = 312044.0975 BIP, Total Power = 440442.4163
12 1000 1000
has yet to be covered. Node 2, 3 and 4 are some of the 900 3 15 17 13 900 3 15 17 13
acnandddid2a5te<ndo4d5e.sHfeonrcter,anbsrmoaidssciaosnt.eFffirocimentchyishfiasguβr2e5,>d25β3<5 adn3d5 780000 12 10 5 1 17189 780000 12 10 5 1 117 98
dβα25.>Thβis45is.tThehegreenfoerrael,bneohdaevi2ordoefciudseinsgtobrtoraadncsmasittewffiicthienpcoywaesr 560000 20 1 560000 20 1
25 16 16
adecisioncriterion,whichresultsinreasonablechoice(shortest 400 4 400 4
300 300
distance). 200 14 6 18 200 14 6 18
2
100 2 100
9 9
0 0
C. Algorithm Description 0 200 400 600 800 1000 0 200 400 600 800 1000
(a) (b)
In this section, we introduce our new algorithm, Greedy
Perimeter Broadcast Efficiency (GPBE). Let S denote the Fig. 4. A sample broadcast routing tree by (a) GPBE and EWMA and (b)
BIP.
source node. The GPBE algorithm maintains two sets: C and
F. The set C represents the nodes currently covered by the
transmission range of nodes. The set F represents the set underlyingbroadcastefficiencyinthiscase.3 Alsonotethatthe
of nodes transmitting with nonzero transmit power such that outerpostsweepingonBIPwillproduceexactlythesameresult
F ⊆C. as in Fig. 4(a).
Due to limited space, we can not provide the results for
GPBE (Greedy Perimeter Broadcast Efficiency) Algorithm directionalantennacase.Instead,interestedreadersarereferred
C :={S}, F :=φ to [6], where we discussed that the same principle utilizing the
PTX(i):=0 for all i∈N broadcast efficiency can be equally well suitable for traditional
while (C (cid:9)=N) sectored antennas or switched beam smart antenna systems.
for each node i∈C and j ∈N\C
find a pair (i∗,j∗) such that V. SIMULATIONMODELANDRESULTS
(cid:15) (cid:16) In this section, we perform simulations with the following
(i∗,j∗)= argmax |ℵi\C| (11) model. Within a 1×1 km2 square region, the network configu-
(i,j)∈C×N\C Pij rations (locations of nodes) are randomly generated according
to uniform distribution. The same random seeds are used for
end a valid comparison of each algorithm. The transmit power
PTX(i∗):=Pi∗j∗ is calculated with normalized proportionality constant (hence,
F :=F ∪{i∗}, C :=C∪ℵi∗ Pij =dαij) and the receiver sensitivity threshold is assumed to
end be0dB.Asapathlossfactor,α=2isused.Broadcastrouting
(cid:17)
return PTX(T):= i∈F PTX(i) trees rooted at the source node (also located randomly in the
grid) are constructed using various algorithms. The simulation
Fig.4(a)showsthefinaltreeGPBEalgorithmproducesfora results are for stationary (non-mobile) network topologies. We
specific topology of 20 nodes. The source node 1 is located at do not limit on the maximum transmit power Pmax as in [1],
thecenterofdeployregion(500,500).Initially,C ={1},F = [2].
φ. At the first iteration, node 1 (i∗ in the pseudocode) picks Fig. 5(a) summarizes the performance comparison of static
the node 11 (j∗ in the pseudocode) as a destination node, trees, MST, BIP, EWMA and GPBE in terms of total
because PTX(1)=P1,11 gives maximum broadcast efficiency. transmit power for various sizes of the networks |N| =
At this stage, each set becomes C = N\{12,13},F = {1}. {20,40,60,100,150,200,300}. Each point in Fig. 5(a) and
Notice how multiple nodes can be added to C simultaneously 5(b) represents an average value of 100 different randomly
with a single iteration. At the next stage, all combinations of generated network topologies. Note that the total transmit
broadcast efficiency βij for (i,j) ∈ C ×{12,13} are tested. power of these algorithms depends solely on the locations of
With the same reasoning provided in Example 2, β11,13 has nodes. To facilitate easy comparison with previous work [1],
the maximum broadcast efficiency. Now each set changes to [2],weusethenormalizedtotaltransmitpower[1]asametric:
C =N\{12},F ={1,11}.Similarly,atthefinalstage,β10,12 Pnorm(T )= PTX(Talgorithm) ,
iCss=elecNte.dUansduatlhlye,atlhgeorigthremedtyermdeinciastieosnin(m3aixteirmatuimonsb,rboeacdacuasset TX algorithm mini∈algorithm{PTX(Ti)}
wherealgorithm={MST,BIP,EWMA,GPBE}.Thecurvesin
efficiency) is made at the perimeters of transmission range,
Fig.5(a)coincidewiththeresultspresentedintheperformance
thatiswhyitiscalledGPBE.Inthisspecificexample,EWMA
evaluation section of [2], which verifies the correctness of
produces the same result.
For the same topology, we also applied BIP algorithm
3Wehavechosenthistopologytofacilitatetheexplanationofouralgorithm.
which results in Fig. 4(b). Clearly, BIP could not exploit the BIPalgorithmperformscomparablyingeneral,ifnotbetter.
1.12.52 Normalized Total Transmit Power,α = 2 MBEGIWPSPBTMEA 111...456 Normalized Total Transmit Power, α = 2 MBEGIWPSPBTMEA ss|ℵtoria\ttheCag|ty=oonf1lcy.hWoaoistshiinngtghlaiesnncoeodwneswtnraiotidhnetm,ipasixcickmoivnuegmreabdrn,ooaid.deec.,atsoitnmef(afi1x1cii)me,nificzyxe
Normalized Power11..101.551 Normalized Power111...123 twihsheitchbherocbaaadnsciacbsaetllyreefafitchcheieednocpwyeriatihtsiomenqinuoiifmvauMlmenStTtr.atonWsmchhaiottopissoinwignerte,arwesnhtoiincdhge
1
1 in the simulation results is that GPBE is an enhancement to
0.9
MST algorithm using more general cost metric. This point
0.950 50 100 150 200 250 300 0.80 50 100 150 200 250 300
Network Size Network Size immediatelyraisesaninterestingquestion:willitbepossibleto
(a) (b) enhancetheperformanceofBIPalgorithmbyrelaxingthecost
metricofBIPalgorithm,analogously?NotethatBIPalgorithm
Fig.5. ComparisonoftotaltransmitpowerofMST,BIP,EWMAandGPBE.
Meanof100randomtopologies.(a)SourceSislocatedatrandom(b)Source uses the incremental power ∆Pjik as a cost metric. We can
S ischosenastheclosestnodefromthecenter(500,500). imagine the relaxed cost metric as |ℵi\C|/∆Pjik, which we
refer as incremental broadcast efficiency. We intend to study
this cost metric in the near future.
implementation. In addition, our new algorithm GPBE is com-
paredtogether.Intermsoftotaltransmitpowerperformance,on
VI. CONCLUSIONS
average,itliesinbetweenBIPandMST.TheEWMAproduced
the best performance in all cases. Inthispaper,wepresentedanovelpower-efficientbroadcast
InFig.5(b),wepickthenodenearesttothecenter(500,500) routing algorithm which effectively exploits the broadcast effi-
as the source node S to test the effect of broadcast efficiency, ciency.WedemonstratedthatGPBEalgorithmhastheproperty
while leaving all other conditions unchanged. In this case, that adaptively assigns transmit power to each node depending
we can observe that GPBE produced better performance than on how densely nodes are distributed, and has the favorable
BIP,becauseGPBEexploitsthebroadcastefficiency.Therefore, ability of choosing multiple nodes at the same time. Although
GPBEcanbeconsideredwithintheregimeofapower-efficient our algorithm GPBE is based on a different philosophy, the
algorithm. This result also suggests that there is some correla- performance of it is comparable to the one of the most
tion between the broadcast efficiency and the construction of prominent power-efficient algorithm in the literature, BIP.
power-efficient broadcast routing problem. Hence, it is worth Our future research direction includes the analysis of com-
further exploration. putational complexity of GPBE, a distributed implementation,
In our simulation results, we observed that about half of the the reduction of search space using the perimeter behavior
cases out of 100 different topologies, GPBE performed better and further enhancement of the algorithm to achieve better
than BIP. But the variance of total transmit power of GPBE performance.
was larger. Hence, this contributed to slightly worse average
performance than BIP, when the location of the source node REFERENCES
is random. This happens especially when the source node is
[1] J.E.Wieselthier,G.D.Nguyen,andA.Ephremides.“OntheConstruction
locatedatthecornerofthedeployregion.Insuchcase,alotof ofEnergy-EfficientBroadcastandMulticastTreesinWirelessNetworks,”
transmit power is wasted before reaching some nodes near the Proc.IEEEINFOCOM2000,pp.586–594.
[2] M. Cˇagalj, J.-P. Hubaux, C. Enz, “Minimum-energy broadcast in all-
center, because at the initial stages of GPBE algorithm, there
wireless networks: NP-completeness and distribution issues,” MOBI-
is less competition among the nodes to find better broadcast COM’02,Sep.2002,Atlanta,Georgia,USA.
efficiency. In fact, GPBE algorithm makes the most aggressive [3] R.RamanathanandR.Rosales-Hain,“Topologycontrolofmultihopwire-
less networks using transmit power adjustment,” Proc. IEEE INFOCOM
choice at each step. We expect some mechanism to control
2000,March2000.
theaggressivenessattheinitialstage,whatwecallaslowstart [4] I. Kang and R. Poovendran, “Maximizing static network lifetime of
mode,willimprovetheperformanceofthealgorithm.Also,the wireless broadcast adhoc networks,” IEEE ICC’03, May, 2003, Alaska,
USA.
problem can be somewhat remedied if each node is equipped
[5] I.KangandR.Poovendran,“Acomparisionofpower-efficientbroadcast
with a directional antenna. This is because, when each antenna routingalgorithms,”IEEEGLOBECOM2003,SanFrancisco,CA,2003.
beamispointedintothedeployregion,thebroadcastefficiency [6] I.KangandR.Poovendran,“S-GPBE:apower-efficientbroadcastrouting
algorithm using sectored antenna,” Proc. IASTED WOC ’03, Banff,
is almost uniform regardless of node location.
Alberta,Canada,2003.
Ontheotherhand,whenthesourceislocatednearthecenter [7] P.J.Wan,G.Calinescu,X.Y.Li,andO.Frieder,“Minimum-energybroad-
cast routing in static ad hoc wireless networks,” Proc. IEEE INFOCOM
of deploy region, as observed in Section IV-A, the broadcast
2001.
efficiency plays an important role and GPBE performs better [8] A.E.F.Clementi,P.Crescenzi,P.Penna,G.Rossi,P.Vocca,“Aworst-case
than BIP. This suggests that GPBE algorithm is more suitable analysisofanMST-basedheuristictoconstructenergy-efficientbroadcast
trees in wireless networks,” Technical Report 010 of the Univ. of Rome
for base station or access point (e.g., such as in IEEE 802.11b
Vergata,2001.
wireless LAN standard) scenarios, where nodes are aggregated [9] M. Bhardwaj, T. Garnett, A.P. Chandrakasan, “Upper bounds on the
around access points at the center. lifetimeofsensornetworks,”IEEEICC’01,Jun.2001.
From a different perspective, we can consider the GPBE
algorithm as a generalization of MST algorithm. Consider a