Efcient and Resilient Backbones for Multihop Wireless Networks

14 Pages·2008·0.25 MB·English

1
Ef(cid:2)cient and Resilient Backbones for Multihop Wireless Networks
Seungjoon Lee Bobby Bhattacharjee Aravind Srinivasan Samir Khuller
Abstract—We consider the problem of finding “backbones” battery-powered,theuseoflow-batterynodesinthebackbone
in multihop wireless networks. The backbone provides end-to- can shorten the overall network lifetime. Therefore, many
end connectivity, allowing non-backbone nodes to save energy
schemeshavebeenproposedthatconsidertheresidualbattery
since they do not have to route non-local data or participate in
powerinselectingbackbonenodes[7(cid:150)9].However,alongwith
the routing protocol. Ideally, such a backbone would be small,
consist primarily of high capacity nodes, and remain connected thebatterycapacity,theseschemesoftenalsouseothercriteria
even when nodes are mobile or fail. Unfortunately, it is often for including nodes in the backbone (e.g., randomized node
infeasibletoconstructabackbonethathasalloftheseproperties; selection for arbitration [7]). This leads to the inclusion of
e.g.,asmalloptimalbackboneisoftentoosparsetohandlenode
low-capacitynodesintheresultingbackbone.Clearly,asmall
failures or high mobility.
backbone composed of high-capacity nodes can signi(cid:2)cantly
Wepresentaparameterizedbackboneconstructionalgorithm
that permits explicit tradeoffs between backbone size, resilience increasetotalnetworklifetime;theconstructionofsuch back-
to node movement and failure, energy consumption, and path bones is the subject of this paper.
lengths. We prove that our scheme can construct essentially Theoperatingenvironmentsformultihopwirelessnetworks
best possible backbones (with respect to energy consumption
can vary widely (e.g., minimal node mobility in sensor or
and backbone size) when the network is relatively static. We
rooftop networks [10] vs. higher mobility for rescue op-
generalize our scheme to build more robust structures better
suitedtonetworkswithhighermobility.Wepresentadistributed eration). Ideally, a backbone construction algorithm should
protocol based upon our algorithm and show that this protocol work well in a wide range of network environments. In
buildsandmaintainsaconnectedbackboneindynamicnetworks. some existing backbone construction algorithms, nodes use
Finally, we present detailed packet-level simulation results to
only local information to build and maintain a backbone
evaluate and compare our scheme with existing energy-saving
quickly [2, 7(cid:150)9]. Although this class of backbone algorithms
techniques. Our results show that, depending on the network
environment,ourschemeincreasesnetworklifetimesby20–220% can be useful in dynamic networks, they do not provide any
without adversely affecting delivery ratio or end-to-end latency. guarantee on performance objectives such as backbone size
or node capacity. Other backbone construction schemes (cid:2)nd
IndexTerms—C.2.2NetworkProtocols,C.2.8MobileComput-
ing, C.2.8.a Algorithm/protocol design and analysis a (cid:147)good(cid:148) connected backbone, e.g., with provable bounds
on backbone size or control overhead. However, this second
class of algorithms typically have higher control overhead,
I. INTRODUCTION requirelongerconvergencetimes,anddonotprovideef(cid:2)cient
In multihop wireless networks, end-nodes are typically mechanisms for backbone maintenance [3, 4]. Therefore,
responsible for relaying traf(cid:2)c [1]. However, we often utilize they are most useful in static environments, but in dynamic
a (cid:147)connected dominating set(cid:148) of nodes that form a routing networks, the overhead of maintaining a (cid:147)good(cid:148) backbone
backbone [2, 3]. Nodes not in the backbone have at least can be prohibitive. Due to such inherent heterogeneities in
one backbone neighbor (hence the backbone is a dominating the operating environmentsformultihopwireless networks, it
set). Further, since the non-backbone nodes do not need to is unlikely that a single (cid:2)xed algorithm will work best in all
route traf(cid:2)c for other nodes, they can save energy by not situations.Inthiswork,wedevelopageneralsolutionthatcan
participating in the routing protocol. If the hardware permits, be tailored to particular network environments.
thenon-backbonenodescan furthersaveenergybyenteringa Thecontributionsofthispaperareasfollows.(i)Wepresent
power-save or sleep mode, only waking up to send messages a parameterized backbone construction algorithm,which per-
or check for pending messages. Smaller backbones lead to mitsexplicittradeoffsbetweendifferentperformancemeasures
greateroverallenergysavings; as such,there havebeenmany including backbone size, resilience to node movement and
algorithmsdevelopedforconstructingnear-optimal connected failure, node capacity, and path lengths. Our scheme has two
dominating sets in wireless networks [3(cid:150)6].1 The problem of logical steps. First, each node nominates its highest-capacity
focusing only on the backbone size is that when nodes are neighbor as its (cid:147)leader.(cid:148) Next, we connect these leaders such
that the resulting backbone achieves speci(cid:2)c ef(cid:2)ciency and
S. Lee is with AT&T Labs, Research (Email: [email protected]). resilience properties. (ii) We prove that our scheme can con-
B. Bhattacharjee, A. Srinivasan, and S. Khuller are with the
structessentiallybestpossiblebackboneswithrespecttonode
Department of Computer Science, University of Maryland (Email:
fbobby,srin,[email protected]). S. Lee and B. Bhattacharjee were capacity and backbone size. To the best of our knowledge,
supported in part by NSF Awards CNS-626636, CAREER ANI-0092806, this is the (cid:2)rst workthat achievesboth objectivesat the same
and a fellowship from the Sloan Foundation. A. Srinivasan was supported
time. (iii) Based upon our backbone construction algorithm,
in part by NSF Award CCR-0208005, NSF ITR Award CNS-0426683, and
NSF Award CNS-0626964. Part of his work was done while on sabbatical we present a distributed protocol that builds and maintains
attheNetworkDynamicsandSimulationScienceLaboratoryoftheVirginia a connected backbone in dynamic networks where nodes are
Bioinformatics Institute, Virginia Tech. S.Khuller was supported in part by
mobile,andnodecapacityconstantlychanges.(iv)Wepresent
NSFgrantsCCF-0728839andCCF-0430650.
1Ingeneral,(cid:2)ndingaminimumconnected dominating setisNP-hard. simulation results that investigate different performance as-
2
pects of our proposed algorithm, including backbone size,
networklifetime, backbone-nodecapacities, and path lengths. G, 4 H, 2 J, 7 G, 4 H, 2 J, 7
Compared to previous energy-saving techniques, our scheme Leader weight = 2
increases network lifetimes by 20(cid:150)220% without adversely D, 5 E, 1 F, 9 D, 5 E, 1 F, 9 X weight = 1 Y
affecting data delivery or end-to-end latency.
weight = 3
Roadmap.Wepresentthe(cid:2)rstphaseofouralgorithm(leader A, 6 B, 3 C, 8 A, 6 B, 3 C, 8
nomination) in x II and the second phase (leader connection) Fragment X Fragment Y Fragment X Fragment Y
in x III. We present our distributed protocol in x IV and
Fig. 2. Multi-
simulationresultsinxV.Wecompareourschemewithrelated (a)Leaderselection (b)Fragments graph
work in x VI and concludein x VII. Please see the Appendix representation of
Fig.1. Leadernominationandresultingfragments. Figure 1(b).
for proofs omitted in the body of the paper.
II. LEADERNOMINATION
assumptions. Recall that a dominating set DS of G = (V;E)
In this section, we (cid:2)rst describe how each node nominates is a subset of V, where each node in V either is in DS or
a leader in the initial phase of our algorithm, and then show has a neighbor in DS [6]. If all nodes in DS are connected,
desirable properties of the resulting set of leaders. We defer thenitiscalledaconnecteddominatingset(CDS).Aminimum
the description of connecting the leaders to Section III.
(connected)dominatingsetisofsmallestcardinalityamongall
We assume the network is connected and model it as (connected) dominating sets. We de(cid:2)ne a maximum-capacity
undirectedgraphG=(V;E),whereV isthesetofnodes,and (connected)dominatingsetDS tobea(connected)dominat-
M
E is the set of edges between nodes. (We discuss the issue ingsetthatmaximizesthebottlenecknodecapacity.Formally,
of uni-directional links in Section IV.) We denote the total DS satis(cid:2)es:
M
numberof nodes in the networkby n=jVj. We de(cid:2)ne N(v)
tobethesetofneighborsofnodev,andN+(v)=N(v)[fvg. 8DS;minv2DSM cv (cid:21)minu2DScu; (1)
We denote v’s degree by dv =jN(v)j, and (cid:1)=maxv2V dv.
A node v has a unique ID and a capacity value c . Although where DS denotes a (connected) dominating set.
v
we can consider various attributes for c (e.g., CPU speed,
v
Theorem 2.1: L is a maximum-capacitydominating set.
storagespace),wefocusonthebatterycapacityinthispaper.2
Proof: L is a dominating set by construction.We prove
themaximum-capacitypropertybycontradiction.Assumethat
A. Algorithm Description
L is not a maximum-capacity dominating set. Consider a
We assume that each node knows the capacity value of maximum-capacitydominatingsetDS .Then,theminimum-
M
its neighbors. The algorithm proceeds as follows: each node capacity node v 2 L satis(cid:2)es: 8u 2 DS ;c < c . By the
M v u
nominates the node with highest capacity value in N+(v) as leader nomination rule, there exists a node w for which v is
leader.Eachnodetheninformsitsleaderofitsdecision,andall the maximum-capacity node in N+(w). However, DS also
M
nominatednodesconstitutethesetofleaders,whichwedenote hasanodeuinN+(w),andsincev isw’smaximum-capacity
byL.Forexample,inFigure1(a),thenetworkhasninenodes. neighbor,c (cid:20)c , which is a contradiction.
u v
The number in each circle denotes the node capacity (e.g.,
We now show that the expected size of L (denoted by
c = 6). Thin lines between nodes represent wireless links,
A E[jLj]) is small. For the sake of simpler analysis, we (cid:2)rst
while thick lines with arrows represent leader nomination. In
consider the case of D-regular graphs (i.e., 8v; d =D) and
the (cid:2)gure, G nominates D because c = 5 is higher than v
D analyze a more generalized case later in this section. In this
c = 2 and c = 4. As a result, nodes A;C;D;F, and J
H G analysis,weassumec isuniformlydistributedbetween0and
become leaders, as shown in Figure 1(b). (Nodes A and F v
1,andlog((cid:1))denotesthenaturallogarithm.(Weplantoextend
nominate themselves as leader, which we do not show here.)
our analysis for other distributions in the future.)
The above algorithm requires only one-hop neighborhood
information and constant time. A similar clustering scheme Theorem 2.2: Suppose 8v;dv = D for a positive integer
is proposed in [11]. Gao et al. [12] analyze the size of D. Then, there exists a parameter (cid:15)>0 such that:
resulting set using speci(cid:2)c geometrical properties. However,
E[jLj](cid:20)(1+(cid:15))n log(D+1): (2)
their analysis assumes that all nodes have a square-shaped D
communication region of the same size, which is seldom the
Also, (cid:15) can be arbitrarily close to 0 as D increases.
case in practice [10]. We next present new analysis results,
based on more realistic assumptions. Inpractice,wirelessnodesarelikelytohavedifferentnum-
bers of neighbors,and Theorem 2.2 does not hold in general.
However, due to spatial locality in the node distribution, we
B. Properties of the Leader Set L
expect that neighboring nodes in multihop wireless networks
WeshowthatLformsadominatingsetusinghigh-capacity
have a similar number of neighbors. Formally, for a constant
nodes, and that the cardinalityof L is small under reasonable
(cid:11) (cid:21) 1, we de(cid:2)ne G = (V;E) to be (cid:11)-locally-regular if
2Fortheeaseofexposition,weassumedistinctcapacityvaluesthroughout 8(u;v) 2 E; dv (cid:20) (cid:11)du: In a 3-locally-regular graph, for
thispaper.Inpractice, weuseuniqueIDstobreak ties. example,thedegreeofv’sneighborisbetweendv=3and3dv.
3
We now generalize Theorem 2.2 to show that in (cid:11)-locally- InFigure1(b),therearethreevirtualedgesbetweenfragments
regulargraphs,E[jLj]iswithinanO(log(cid:1))-factorofthesize X and Y: the (cid:2)rst one using G and H, the second one using
of a minimum dominating set. E andB,andthelast oneusingB only.Theweightsofthese
Lemma 2.3: Suppose G = (V;E) is (cid:11)-locally-regular for threevirtualedgesare2,1,and3,respectively.Figure2shows
constant (cid:11)(cid:21)1. Then, thecorrespondingmultigraphrepresentation.Wenextdescribe
how we use this multigraph to (cid:2)nd a connected backbone.
1
0
E[jLj](cid:20)c log(d +1);
v
d
vX2V v B. TRUNC-1: Spanning Tree-Based Algorithm
where c0 is a constant that depends on (cid:11). We begin with an approach based on the well-studied
Theorem 2.4: Suppose G=(V;E) is (cid:11)-locally-regularfor minimum spanning tree (MST) problem. This MST-based
constant (cid:11) (cid:21) 1. Then, E[jLj] = O(log(cid:1))OPT, where OPT approach is a special case of our parameterized algorithm
is the size of a minimum dominating set. (SectionIII-C),whichwecall TRUNC-1.RecallthatanMST
of edge-weighted graph G = (V;E) connects all nodes in V
Theorems 2.2 and 2.4 are essentially best possible. Theo- using a tree T (cid:18) E, such that the sum of edge weights in
rem2.2holdsforanyD-regulargraph,andas shownin[13], T is minimized [16]. In many algorithms that (cid:2)nd MSTs,
thereexistD-regulargraphswhoseminimumdominatingsets
nodes select a minimum outgoing edge that does not result
are of size at least (1 (cid:0) (cid:15)0)n logD for (cid:15)0 > 0. As D
D in a cycle [16, 17]. However, since we want to select high-
becomes large, this value becomes arbitrarily close to the capacity nodes in the backbone, we need to use maximum-
upperboundinTheorem2.2.Also,theapproximationratioof weight outgoing virtual edges. For example, in Figure 2,
Theorem 2.4 to OPT is O(log(cid:1)). In general, (cid:2)nding a mini- when connecting fragments X and Y to obtain high-capacity
mumdominatingsetforagivengraphisNP-hard[6].Also,no
connectedbackbone,weshouldusethevirtualedgeofweight
polynomialtimealgorithmcanachievetheapproximationratio
3.WefurtherillustratethisusinganexamplegraphinFigure3:
of(1(cid:0)(cid:15)0)log(cid:1)forany(cid:15)0 >0unlessNPhasnO(loglogn)-time
here, each node corresponds to a fragment after the leader
deterministicalgorithms[14].Thus,theboundinTheorem2.4
nomination phase, and each fragment is connected by virtual
is withina constantfactorofthebest-possibleapproximation.
edges. (We show only the maximum-weight virtual edges
Although other existing schemes provide certain theoretical
between fragments for clarity.) Figure 4 shows the MST (as
guarantees about resulting dominating sets, some rely on
de(cid:2)ned above).
sequentialoperationonanentirenetworkormultipleroundsof Let B1 denote the connected backbone obtained by using
local operation[3, 4,15],whichcan delaythe dominating-set TRUNC-1.WenextshowthatB1producesasmallconnected
formation in distributed environments. Some other analytical backbone using high-capacity nodes.
resultsarebasedoncertainsimpli(cid:2)edassumptions[4,12].We
Theorem 3.1: TRUNC-1 results in a maximum-capacity
useonlyoneroundoflocaloperationandprovidean analysis
connected dominating set.
for generalized settings that relate to realistic distributed
environments. Lemma 3.2: jB1j(cid:20)3jLj, whereL denotestheleader set.
Proof: If L has f fragments, we need (f (cid:0)1) virtual
edges for a spanning tree. Since each virtual edge has up to
III. CONNECTINGTHELEADERS
two nodes and f (cid:20)jLj, jB1j(cid:20)jLj+2(f (cid:0)1)(cid:20)3jLj.
We now present the second phase of our algorithm that
FromthelemmaandTheorem2.4,thenexttheoremfollows.
connects the leaders to form a connected dominating set.
We describe a special case of our scheme and then present Theorem 3.3: For (cid:11)-locally-regular graphs, E[jB1j] =
O(log(cid:1)) OPT, where OPT denotes the size of a minimum
the general scheme (called TRUNC-K, where K is a system
connected dominating set.
parameter).
Discussion: Theorem3.1 states thatB1 includesa node
with low capacity only when it is necessary in maintaining
A. Multigraph Representation
connectivity. We show in Theorem 3.3 that for (cid:11)-locally-
The set of leaders form a forest in which edges are leader-
regular graphs, B1 is an O(log(cid:1))-approximation to a min-
nomination relations. We refer to each tree in this forest
imum connected dominating set. As discussed in Section II,
as a fragment. For example, in Figure 1(b), there are two
thisiswithinaconstantfactorofbestpossibleapproximation.
fragments: fragment X (nodes A and D) and fragment Y
However, if a maximum-capacity backbone of even smaller
(nodes C, F, and J). Since L is a dominating set, as shown
size is desired, we can further reduce the constant factor by
in [6], chains of up to two non-leader nodes are suf(cid:2)cient to
using the following optimization. When the B1 is found, we
connect all fragments. We de(cid:2)ne a virtual edge to be such
gettoknowtheminimumnodecapacityinthebackbone(say,
a chain of (up to two) non-leader nodes that connects two
c ). Then, we apply any distributed CDS algorithm [3, 4]
th
fragments. We transform the graph into a multigraph, where
onto a restricted set of nodes v where c (cid:21)c . For example,
v th
eachfragmentcorrespondstoavertexwith(possiblymultiple)
by applying the scheme in [3], the approximation ratio of
virtual edges connecting fragments. For a given virtual edge,
the resulting maximum-capacity backbone becomes at most
weusetheminimumnodecapacityastheweightoftheedge.3
2log(cid:1)+3. (See the last part of the Appendix.)
3Itispossiblethatnonodesareinvolvedinavirtualedge.Inthiscase,we Although TRUNC-1 backbones achieve our desired goals
settheweightofthevirtual edgeto1. (i.e., (cid:2)nding a small backbone using high-capacity nodes),
4
9 A1 4 11B 5 E 9 A 11B 5 E 9 A1 4 11B 5E 9 A 4 11B 5E
C D 10 C D 10 C D 10 C D 10
7 6 3 H 7 6 H 7 6 3 H 7 6 H
F 8 G 2 F 8 G F 8 G 2 F 8 G 2
Fig.3. Examplegraph. Fig.4. TRUNC-1backbone (a)After(cid:2)rstround (b)Resultingbackbone(B1)
Fig.5. Illustration oftruncated algorithm.
Algorithm 1 Truncated Algorithm (Centralized) in this example,each remainingfragmentafter the (cid:2)rst round
1: Round 0 connectsto all neighboringfragments.For example,fragment
2: while more than one fragment exists do FG chooses three edges to fragments AC, BD, and EH. The
3: if Round = K then resulting connected backbone is shown in Figure 5(b).
4: Merge with all neighboringfragments WecallthisalgorithmTRUNC-Kandtheresultingbackbone
5: Return B . In contrast to O(logn) rounds in Boruvka’s algorithm,
K
6: end if TRUNC-K needs only a constant number (K) of rounds to
7: Each fragment selects the best outgoing edge complete, and the resulting backbone has higher redundancy
8: Merge fragments using the selected edges than B1. This eventually leads to both increased resilience
9: Round Round + 1 against node mobility and decreased average path length.
10: end while Note that the resulting backbone is not a maximum-capacity
backbone and may include low-capacity nodes. However, by
construction, nodes included in the (cid:2)rst K rounds are part
the running time can be long. For example, a distributed of a maximum-capacity backbone. After the K-th round,
MST algorithm by Gallager, Humblet, and Spira (the GHS whenconnectingtoeachofremainingneighboringfragments,
algorithm) takes O(nlogn) running time [17]. Also, there we choose the best virtual edge among typically multiple
is a clear trade-off between small backbones and shorter edges, and we include relatively high-capacity nodes. Also,
path lengths as well as resilience. In Figure 4, the backbone the resulting backbone includes more virtual edges than B1,
becomes disconnected even when a single link fails. Also, to and Theorem 3.3 does not hold. However, we can adjust
reach a node in fragment G, a node in fragment H needs to K to control the amount of increase. Our future goal is
use a path consisting of (cid:2)ve virtual edges, compared to only to analyze the performance trade-offs (e.g., backbone size,
one when no backbone is used. We address this issue next. capacitydistribution)whenwevaryK.Wenextusesimulation
experimentstoillustratethatevenwith smallvaluesofK,the
increase in backbone size is not signi(cid:2)cant.
C. TRUNC-K: Parameterized Algorithm
We now describe our generalized scheme that balances
D. Evaluation of the TRUNC-K Algorithm
the above-mentionedtrade-offwhen connectingthe leader set
(Algorithm 1). It is based on a well-known MST algorithm Inthissubsection,weusesimulationstounderstandperfor-
byBoruvka[18].InBoruvka’salgorithm,eachfragment(cid:2)nds mance trade-offs of the TRUNC-K algorithm (e.g., backbone
and marks the best outgoing edge. Then, using those edges, size, capacity) when we use different values of the parameter
fragments are merged into new larger fragments. This step is K. In this simulation, stationary nodes are distributed on a
repeateduntilthereisnooutgoingedge(i.e.,thereisonlyone squareuniformlyatrandom,andwevarythenumberofnodes
fragment). During the (cid:2)rst K rounds, our algorithm runs just and the size of square to experiment with various settings.
as Boruvka’s algorithm, where K is an algorithm parameter. Node capacity values are uniformly distributed between 0
However,in our truncated algorithm,all remaining fragments and 1. Nodes within the nominal transmission range (250
after K rounds mark edges to all neighboring fragments and meters)becomeneighbors.Foreachsetofparameters,weuse
are merged into one fragment. One extreme case is K = 25runswithdifferentnodeplacementscenariosandreportthe
0, where after leader nomination, each pair of neighboring average. We also experimented using various scenarios with
fragmentsmarksonevirtualedge(e.g.,alledgesinFigure3). non-uniform node placement and different capacity distribu-
Another extreme case is K =1, which results in B1. tion, and obtained similar results. (See Section V.)
Figure 5 shows the operations of the algorithm applied to Backbone Size: In Figure 6, we show the average size of
the graph in Figure 3. Here, we set K = 1. In the (cid:2)rst the backbone with varying K. We use two different network
round, each individual fragment selects the best outgoing settings(cid:151)the one with 1000 nodes on a 2km(cid:2)2km square,
edgeamongneighboringfragments,andfragmentsaremerged and the other with 4000 nodes on a 4km(cid:2)4km square. In
using selected edges. Then, as shown in Figure 5(a), there Figure 6, the use of extra rounds is most effective when K
remain four fragments at the end of (cid:2)rst round. Since K =1 is small. Speci(cid:2)cally, the (cid:2)rst round (K = 1) leads to the
5
1000 nodes placed in a 4km(cid:2)4km square. When there is no
600 4000 nodes in 4km by 4km square
1000 nodes in 2km by 2km square backbone, the average path length is 11.2. The use of any
500 routing backbone inevitably increases path length since we
are forced to (cid:2)nd paths using a restricted set of nodes. B
0
e 400
Siz hasmostredundancy,andtheaveragepathlengthis12.5with
one 300 minimumincrease.As K increases,theredundancydecreases
b
ack and the path length thus increases; the average path length of
B
200 B is 14.8, while that of B is 18.8. In contrast, the average
1 2
expansion in path length for B1 is 23.0, which is more than
100
twice the underlyingshortest paths. We observe that small K
valuesagainofferagoodtrade-off.Forexample,comparedto
0
0 1 2 3 4 5 6 7 8 B1,theaveragepathlengthofB1 isupto36%shorter,while
Number of Rounds (K)
the backbone size is only up to 13% larger.
Fig. 6. Backbone size with different K values. The error bars represent To summarize, backbones obtained using small K (1 or
standard deviations. 2) perform well and provide a reasonable balance among
a number of performance measures. We next describe a
1.4km(cid:2)1.4km 2.0(cid:2)2.0 2.8(cid:2)2.8 4.0(cid:2)4.0 distributed protocolthat implementsthe TRUNC-K algorithm.
min. avg. min. avg. min. avg. min. avg.
B0 0.349 0.913 0.111 0.854 0.021 0.771 0.007 0.666 IV. DISTRIBUTEDPROTOCOL DESCRIPTION
B1 0.860 0.967 0.705 0.934 0.307 0.872 0.054 0.760
B2 0.888 0.970 0.787 0.942 0.573 0.892 0.188 0.796 In this section, we present our distributed protocol that
B1 0.888 0.970 0.787 0.942 0.574 0.893 0.200 0.802 implementstheTRUNC-Kalgorithmtoconstructandmaintain
TABLEI a connectedbackbonein dynamic networkenvironments.Our
CAPACITYVALUESOFBACKBONENODESWITHVARYINGNODEDENSITY protocolisbasedontheGHSalgorithm,whichisadistributed
version of Boruvka’s algorithm [17]. We assume that each
node has a unique ID (e.g., IP address). We (cid:2)rst describe
the leader nomination and explain how to connect the frag-
largest reduction in backbone size. With larger K > 2, there
ments obtainedafter the nominationphase. We also present a
are a small number of remaining fragments after K rounds.
backbonemaintenancemechanismlater in this section. These
Asaresult,whencomparedtoB1,connectingallneighboring
backbone construction operations are performed periodically.
fragments does not signi(cid:2)cantly increase the backbone size.
Whiletheintervaldependsonvariousfactorssuchasmobility,
CapacityDistribution amongBackboneNodes: We investi-
nodedensity,traf(cid:2)cpattern,etc.,oursimulationsinSectionV
gateanotherpotentialproblemwith TRUNC-Kbackbone(cid:151)the
indicate that 10(cid:150)20 seconds works well in typical scenarios.
resulting backbone may include low-capacity nodes. In this
scenario, we use 1000 nodes but vary the square size, thus
A. Leader Nomination Protocol
varying node density. In Table I, we list the minimum and
averagecapacityvaluesdependingforK valueswithdifferent Each node broadcasts a HELLO message periodically that
node density. Even with small K (1 or 2), the difference in includes information about itself and its neighbors. Figure 7
minimum-capacitybetweenBK andB1issmall.Forexample, shows the (cid:2)elds for individual node information in HELLO
inthecaseof2km(cid:2)2kmsquare,thedifferencebetweenB and messages.Usingthese(cid:2)elds,eachnodemaintainsinformation
1
B1isaround10%(0.705vs.0.787).Thedifferenceinaverage about two-hop neighbors (e.g., capacity, fragment root IDs).
capacity values is even smaller: less than 1% for the same Before broadcasting a HELLO message, node v checks
scenario.AsdiscussedinIII-C,thisisbecausefragmentsafter whichneighborhasthehighestcapacity(e.g.,residualbattery
K roundschoosebestpossiblevirtualedgestoconnectneigh- power).Supposeuisthehighest-capacityneighborofv.Then,
boring fragments, and very low-capacity nodes are not likely v sets its Leader ID (cid:2)eld to u in its HELLO message. Upon
to join the backbone. However, in sparser networks, fewer receiving a HELLO message from v, u becomes a leader and
virtualedgesareavailablebetweenneighboringfragments,and setsitsIsLeader(cid:2)eldtoTRUEinsubsequentHELLOmessages
the difference in minimum capacity between BK and B1 is until v changes leaders and there exist no other neighbors
slightly larger.4 In the actual deployment of the TRUNC-K nominating u (e.g., due to later decrease in residual battery).
algorithm,weshouldchooseanappropriateK valuebasedon Suppose node u (cid:2)nds itself as the highest-capacity node in
network parameters such as node density and mobility. N+(u). Then, in addition to being a leader, u also becomes
AveragePathLength: Weconsidertheaverageshortestpath a level-0 fragment root, where a level-0 fragment is a set
length(inducedbythebackbone)betweeneachofallpossible of leaders who are themselves connected via the leader-
node pairs. This measure provides a good lower bound for nominationrelation.InFigure1(b),nodesAandF arelevel-0
the performance of practical routing protocols such as [1]. fragment roots.
Due to space constraints, we report results for the cases with
B. Protocol for Fragment Members
4When 5km(cid:2)5kmsquares areusedwith 1000 nodes, only fourcasesout
As discussed in Section III,the set of leaders forma forest
of25resultedinconnectednetworks,andtheuseof4km(cid:2)4kmsquareswith
1000nodescorrespondstoconsiderably sparsescenarios. consisting of multiple fragments, and the protocol described
6
Fragment Root Algorithm 2 Distributed operation of level-i fragments
NIoDde Capacity IsLeader LeIaDder Level-0 ... Level-K 1: Level-i fragment root periodically sends REQi message
2: FragmentmemberssendREPLYi messageswithneighbor-
Fig.7. Information aboutindividual nodesina HELLOmessage. ing level-i fragment information
3: if level-i fragmentroot receives all REPLYi messages, or
a timeout occurs then
4: if i = K then fhighest levelg
heremergesthe fragmentsto formoneconnectedcomponent. 5: Fragment root sends CONNECTi messages to all
In Algorithm 2, we present a high-level protocol description. neighboringlevel-i fragments
We begin with the operation of level-0 fragments and later 6: else f i<Kg
discuss the operation of higher-level fragments. 7: FragmentrootsendsCONNECTi messageonlytobest
We illustrate the protocol operations of level-0 fragments neighboringlevel-i fragment
using Figure 8. Each level-0 fragment forms a tree rooted 8: end if
at its fragment root. To discover neighboring level-0 frag- 9: end if
ments, level-0 fragment roots periodically send REQ0 mes-
sages, which are forwardeddown this tree to the leaves (who
cannot forward the REQ message any further). The leaves still send REQi messages periodically.This allows lower-level
then generate a REPLY0 message that contains information fragments to (cid:2)nd new or better virtual edges to neighboring
aboutotherfragments (ifany)thattheyare connectedto.The fragments in dynamic networks.
REPLY0 messages are forwarded back towards the fragment
root.Forexample,inFigure8(b),nodeD generatesa REPLY0 C. Backbone Maintenance
message, which contains the ID of other level-0 fragments
that D knows of (F in this example) along with the cost All of the protocol speci(cid:2)c states (e.g., leaders, bridges,
y
of the virtual edge to connect to F . (Recall that D keeps fragment roots) are (cid:147)soft.(cid:148) A node removes a neighbor if it
y
the information about fragment roots of two-hop neighbors.) does not receive a HELLO message from the neighbor for a
At each hop, before forwarding the REPLY message towards certainduration(e.g.,fourHELLO-PERIODs).Ifthecapacityof
the leader, nodes update the message if they know of a better the leader becomes lower (e.g., due to battery consumption),
virtual edge than the one carried in the message. Also, nodes a node may choose a different node with highest capacity as
addinformationaboutanynewneighboringfragmentsthatare leader.Ifaleader(cid:2)ndsthatnoneighborsnominateitasleader
not in the REPLY message. In our example, node B does not forsometime,itstopsbeingaleader.Whenabridgedoesnot
modify the REPLY message from D, since its path to Fy is receive a CONNECT message for a certain period of time, it
worsethantheonethatD found(Figure8(b)).(AandC also stops being a bridge.
send REPLY0 messages, which are not shown in the (cid:2)gure.) In a dynamic network, however, the basic protocol mecha-
Once the fragment root has accumulated all REPLY mes- nisms described above may not be suf(cid:2)cient for the timely
sages (or has timed out on some), it sends a CONNECT maintenance of the connected backbone. We ef(cid:2)ciently re-
messageusingthebestoutgoingvirtualedge.Thisisshownin construct the backbone using a simple local search protocol
Figure 8(c), where X connects to Y using the weight 7 edge that exploits spatial locality. We illustrate its operation via an
through D. This virtual edge has two non-backbone nodes example.InFigure9,nodeP detectsalinkfailuretobackbone
P and Q, and upon receiving the CONNECT0 message, they neighborQ. P looksup its neighbortable to (cid:2)ndothernodes
become bridges and join the backbone. Using these bridge that also had Q as neighbor. (Note that these nodes need not
nodes,F andF aremergedtoformanewlevel-1fragment. currently be part of the backbone). In this example, P (cid:2)nds
x y
Level-1 fragments also need to (cid:2)nd neighboring level- twosuchneighbors,M andN,andsendsaRECOVERmessage
1 fragments to form next-level fragments. To elect level-1 toN,whichhashighercapacity.Uponreceivingthismessage,
fragmentrootsthatsendREQ1 messages,weusethefollowing N temporarilyjoinsthebackboneandformsabridgetoQ.In
rulesimilarto[17]:Iftwofragmentschooseeachotherastheir thenextREQ-REPLYphase,X mightchooseadifferentvirtual
best neighboring fragment, then two fragment roots become edge (of higher weight) to connect to Fy. If that happens, N
candidates for the next-level fragment root. We choose the will leave the backbone after a timeout.
node with lower ID as the level-1 fragment root. There are potential problems with the local recovery
Level-i fragments (0 < i < K) operate similarly to above scheme. First, the repaired backbone may include lower-
procedures until their level reaches K. At the highest level- capacitynodes than necessary.However,as mentionedabove,
K, instead of using only the best virtual edge, the level-K inthe next REQ-REPLY phase,thefragmentrootwill discover
fragment roots send CONNECT messages to all neighboring the best virtual edge and send the appropriate CONNECT
level-K fragments, thus assuring a connected backbone. message. Also, a node may not be able to (cid:2)nd a common
In Figure 8, X is a both level-0 and level-1 fragment root, neighbor for recovery. However, in networks with reasonable
and it periodically sends both REQ0 and REQ1 messages. node density, such events will likely be infrequent. Finally,
In general, a node can be a fragment root of up to (K+1) therecoveryschemedoesnothelpwhen nodesfail. However,
levels at the same time. Even if higher-level fragments are the TRUNC-K backbone should have suf(cid:2)cient resilience to
alreadyfound,lower-levelfragmentroots(e.g.,Y inFigure8) maintain connectivity against infrequent recovery failures.
7
REQ Fx Fx Fx
weight=4
X X 2. REPLY X
(Fy:w=7) Fy Fy Fx M,1 Fy
A B A B Y A B Y
1. REPLY CONNECT D U
(Fy:w=7)
P Q
C D C D U C D U
weight=7 P Q N,2
Fig.9. Local maintenance.
(a) REQmessage (b)REPLYmessage (c) CONNECTmessage
Fig.8. Overviewofprotocoloperations.In(b),REPLYmessagecontainsinformationaboutoutgoingvirtualedges.
We examine the effectiveness of this recovery scheme using A. Brief Description of Existing Schemes
simulations in Section V. In SPAN [7], a node becomes a coordinator and joins the
Discussion: As shown in Figure 7, HELLO messages in backbone when any two neighbors are not connected using
TRUNC-K contain (K+3) node IDs per neighbor: Node ID, up to two current coordinators. To minimize contention and
Leader ID,andfragment roots forK+1levels.Forexample,
give priority to high-energy nodes, SPAN uses a randomized
suppose that node U in Figure 8(c) is about to broadcast a
backoff using the energy level, number of neighbors, and a
HELLO message. When K=1, the information for neighbor randomnumber.Acoordinatorwithdrawsaftersomeperiodof
Q should include (Q, U, Y, X). Including more information
timetogiveotherneighborsachancetobecomecoordinators.
in HELLO messages increases the control overhead.However, In GAF [8], the area is divided into square-shaped virtual
since many neighbors share leaders and fragment roots, we
grids. GAF assumes the availability of location information
canreducetheincreasebyusingthefollowingsimpleindexing
(e.g.,fromGPS),andeachnodecanknowitsvirtualgridfrom
scheme. U arranges all neighbors into an array and uses the
thelocationinformation.Then,GAFelectsthehighest-energy
indexvaluesforleaderIDsandfragmentrootsofitsneighbors.
node in each grid, and these elected nodes form a connected
In the above example, U includes the following information
backbone due to the grid construction rule [8].
for its neighbor Q: (Q, I , I , I ). Since an index (cid:2)eld
U Y X In the scheme by Wu et al. [9], a node initially joins the
is typically shorter (e.g., 1 byte) than an actual ID (e.g., 4
backbone if its two neighbors are not connected. Then, to
bytes), the amount of length increase becomes smaller. Note
reducethe size of this initial backbone,node v searches for a
that U still needsto includesome non-neighborIDs (e.g.,X)
neighbor u, or two neighbors u and w, such that the (union
inits HELLO messages.However,since manyofits neighbors of) neighbor set(s) includes the neighbor set of v. Due to
share leaders and fragment roots, the number of such non-
symmetry, the above rule may lead to connectivity loss, and
neighbors nodes are likely to be small. TRUNC-K also uses a theauthorsof[9]alsousethepowerlevelanddegreeofnode.
few additional control messages (e.g., REQ, REPLY), which
can potentially increase the overall control overhead. Our
B. Comparison Study in Large Networks
simulationresultsinSectionV-Cshowthattheoverallcontrol
overhead of TRUNC-K is minimal. In this set of experiments, we use the same settings as in
Wirelesslinksinpracticecanbeuni-directionalandshowa Section III-D. We measure the performance when the initial
widerangeofdifferenceintheir quality[10].Inourprotocol, backbone stabilizes, and report the average of 25 runs each.
we can easily detect uni-directional links using the neighbor We (cid:2)rst examine the size of backbones constructed by dif-
information in periodic HELLO messages and exclude those ferentschemes.Inthissetofexperiments,wevarythenumber
links when building backbones. We further discuss the issue of nodes and the size of square, but maintain the average
of link quality in Section V. node degree constant. In Table II, we present the average
backbone sizes for various scenarios. The standard deviations
V. SIMULATIONSTUDY aresmall (less than6% oftheaveragein allcases), whichwe
Inthissection,wecompareTRUNC-Kwithpriorapproaches donotpresent here.We observethat TRUNC-1backbonesare
using simulation experiments. Based on the results in Sec- smallest in all cases. Speci(cid:2)cally,when the networkhas 4000
tion III-D, we consider onlythe case of K =1. Although we nodes,theTRUNC-1backbonehas355nodesonaverage.This
performedexperimentsinvariousotherscenariosusingdiffer- is 24% smallerthan theSPAN backbone,whichis thesecond
ent topologies, traf(cid:2)c patterns, and capacity distributions, due smallest in all these experiments.
tospaceconstraints,wepresentonlyasubsetofrepresentative Our proposed scheme also builds a backbone consisting of
resultsinthis paper.Whilewefocusmainlyonpriorschemes higher-capacitynodes. In Table III, we tabulate the minimum
that consider node capacity, at the end of Section V-B, we and average capacity values of backbone nodes. In all cases,
also compare TRUNC-K with other existing schemes that do thebackbonebyTRUNC-1achievesthehighestvaluesforboth
not consider node capacity. We (cid:2)rst describe prior capacity- minimum and average node capacity. For example, in 4000-
aware approaches and then compare the performance of our nodenetworks,theTRUNC-1backbonedoesnotincludeanyof
scheme against them. bottom30%nodes,whiletheGAFbackboneincludessomeof
8
No.ofNodes(squaresize inkm(cid:2)km)
Numberofnodes(squaresizeinkm(cid:2)km)
500 1000 2000 4000
500 1000 2000 4000
(1.4(cid:2)1.4) (2.0(cid:2)2.0) (2.8(cid:2)2.8) (4.0.(cid:2)4.0)
(1.4(cid:2)1.4) (2.0(cid:2)2.0) (2.8(cid:2)2.8) (4.0(cid:2)4.0)
min avg min avg min avg min avg
SPAN 54.5 113.9 227.7 467.4
SPAN 0.056 0.700 0.046 0.686 0.025 0.704 0.011 0.708
Wuetal. 67.4 150.3 308.9 652.5
Wuetal. 0.005 0.504 0.002 0.480 0.002 0.495 0.002 0.504
GAF 158.0 308.6 605.6 1236.9
GAF 0.032 0.714 0.014 0.707 0.007 0.720 0.003 0.723
TRUNC-1 44.7 89.0 174.6 355.1 TRUNC-1 0.752 0.937 0.705 0.934 0.502 0.933 0.335 0.933
TABLEII
TABLEIII
BACKBONESIZEBYDIFFERENTSCHEMES.
MINIMUMANDAVERAGECAPACITYVALUESOFBACKBONENODES
Experiments with Non-uniform Node Distribution: In the
300
previous experiments, we placed nodes uniformly at random.
GAF
e 250 In this set of experiments, we (cid:2)rst partition the area into
n
o
ackb 200 squaregrids(witheachside200m)andleteachcellpotentially
n b have a widely varying number of nodes. Speci(cid:2)cally, we
des i 150 Wu randomly choose the node count for each cell using two
o
of n differentdistributions:exponentialandPareto.(Withinasingle
er 100 cell, nodes are randomly distributed.) In Table V, we report
b
m SPAN
u theresultswhenweusea2km-by-2kmareaandtheaverageof
N
50
10 nodes in each cell. We observe that TRUNC-1 consistently
TRUNC-1
outperforms existing schemes when nodes follow different
0
0 200 400 600 800 1000 distribution patterns.
Node rank (sorted in ascending order of capacity value)
Comparison with Capacity-unaware Schemes: While we
Fig.10. Capacity distribution ofbackbone nodesindifferent schemes. have compared TRUNC-1 with prior backbone construction
schemes that consider node capacity, there are other schemes
thatfocusonsmallbackbonesizeorcontroloverheadwithout
considering backbone capacity [3, 4, 19]. Basagni et al. [20]
compare some of them based on multiple criteria, and we
bottom0.5%nodes.Inthesamescenario,theaveragecapacity brie(cid:3)y compare them with TRUNC-1 in terms of backbone
ofTRUNC-1backboneisalso30%higherthanthoseofSPAN size. Whenwe use thesame networksettings, TRUNC-1(cid:2)nds
andGAF.Whentheroutingbackboneisusedtoreducepower smaller backbones than highly localized schemes (e.g., [19]),
consumptionandincreasethenetworklifetime,theuseoflow- while TRUNC-1 backbones are similar in size to those based
capacity nodes can drain their energy unnecessarily. We later onglobaloperation(e.g.,[4]).Forexample,indensenetworks
investigate this aspect using packet-level simulations. (withtheaveragenodedegreebeingaround20),bothTRUNC-
1 and the scheme by Wan et al. [4] include around 19% of
In Figure 10, we present a detailed snapshot of a represen-
nodes in the backbone on average, while backbones by Dai
tativerunwith 1000nodes.We sort all nodes in anascending
and Wu [19] include around 25% of nodes. This is some-
order of capacity value and cumulatively plot the number of
what expected; TRUNC-1 uses information about extended
backbone nodes whose capacity is less than or equal to that
neighborhood (e.g., level-1 fragments) and thus can build
ofa givennode.For example,theGAF backboneincludes49
smaller backbones than purely localized schemes, while the
nodes out of 500 lowest-capacitynodes,while SPAN chooses
difference from the globally sequential scheme by Wan et
19nodesfromthelowest500nodes.Incontrast,theTRUNC-1
al. is minimal (See Section III-C). In addition to small size,
backbone does not include any of the lowest-capacity nodes,
TRUNC-1considersnodecapacity,andtheresultingbackbones
but selects only 93 nodes among the top 330 nodes.
consistmostlyofhigh-capacitynodes.Wenextpresentpacket-
InTableIV,wereporttheaveragepathlengthsbydifferent level simulation results to demonstrate that TRUNC-1 leads
schemes as well as the case using no backbones. Not sur- to signi(cid:2)cant increase in network lifetime, while maintaining
prisingly, since TRUNC-1 backbones are smaller in size than connectivity in dynamic scenarios.
any other scheme (Table II), its average path lengths are the
longest.However,theamountofreductioninbackbonesizeis
C. Packet-level Simulations
more than the increase in the path length, especially in larger
In this subsection, we focus on saving energy and extend-
networks. Speci(cid:2)cally, in 4000-node networks, the difference
ing network lifetime using ns-2 simulations [21]. SPAN and
in the average path length between SPAN and TRUNC-1 is
TRUNC-1 performed best in Section V-B, and we compare
around 20%, while the difference in backbone size is more
only these two schemes here. We use the SPAN simulation
than 30%. The other two schemes (GAF and Wu et al.)
code written by the authors of SPAN.5 Due to high resource
have shorter path lengths on average, but their backbones are
requirements, we have been able to perform simulations only
substantiallylargerinsize(TableII).Thisresultillustratesthat
TRUNC-1backbonesproviderelativelygoodpathsconsidering 5Available at http://www.pdos.lcs.mit.edu/span/. We plan to make our
the small size. simulation codepublicaswell.
9
No.ofnodes(squaresizeinkm(cid:2)km)
Exponential Distribution ParetoDistribution
500 1000 2000 4000
backbone avg. min. backbone avg. min.
(1.4(cid:2)1.4) (2.0(cid:2)2.0) (2.8(cid:2)2.8) (4.0.(cid:2)4.0)
size capacity capacity size capacity capacity
Nobackbone 3.66 5.04 6.86 9.60
SPAN 104.16 0.660 0.017 111.48 0.669 0.025
SPAN 4.39 6.17 8.44 11.89
Wuetal. 118.28 0.494 0.006 131.32 0.507 0.006
Wuetal. 4.14 5.75 7.86 11.01
GAF 272.56 0.699 0.009 298.12 0.689 0.009
GAF 3.93 5.45 7.45 10.46
TRUNC-1 87.76 0.919 0.563 89.84 0.923 0.600
TRUNC-1 5.66 7.84 10.27 14.35
TABLEV
TABLEIV
BACKBONESIZEANDCAPACITYVALUESWITHDIFFERENTNODEDISTRIBUTIONS
AVERAGEPATHLENGTHBYDIFFERENTSCHEMES.
withrelativelysmall topologies(with150nodes).We(cid:2)rstde- 120
scribeoursimulationenvironmentbeforereportingtheresults.
100
1) Simulation Environment: Both TRUNC-K and SPAN
es
run on top of the IEEE 802.11 MAC layer [22], and non- Nod 80
bpp8eae0rcr2iik.oo1bdd1osan.pneAodwnlleoexndrcoehdssaaensvstgiasneytgamyinmeasowtshdaaeegk,epesotiiwtnmoeteihrneifssoabvrepmiganirgnntinetmiiigonohngdbeoedo.frsIeinnaotcofthhpebbeeenIaaEdcciEoonEnng Number of Dead 4600 Half (7N5)o PSM SPAN TRUNCL-1ower Bound
messages. If a node (cid:2)nds that there are buffered incoming 20
messages, it requests the messages and stays awake during
the beacon period. Otherwise, it goes back to sleep until the 0
0 500 1000 1500 2000 2500 3000
start of the next beacon period. Power saving mode usually Time (sec)
leads to increased delay and reduced throughput (e.g., due
Fig.11. Numberofdeadnodesover time.L:M:H=3:4:3.
to additional control packets), and Chen et al. [7] slightly
modi(cid:2)ed the power saving mode in the 802.11 MAC to
improve performance, which we use in our simulations.
Weassumetherearethreeclassesforthenodeenergylevel.
performance. In each case, we report the average of 5 runs.
A low-energy node has 300J of energy, which is used in the
2) Simulation Results: For the (cid:2)rst set of results, we
experiments in [7]. A medium-energy node has 600J, and a
examine two types of network lifetimes [24]. Network 1-life
high-energy node has 2500J. (2500J is usually suf(cid:2)cient to
is the time when the (cid:2)rst node dies, and half-life is the time
last 3000 seconds of simulation time.) We vary the node
when the half of initial nodes die.6 In addition to TRUNC-1
percentage of each class to examine the performance in
and SPAN, we use two other schemes for reference. The (cid:2)rst
differentsettings.Nodeenergyisconstantlyupdatedusingthe
one is to identify a lower bound, in which all nodes always
followingpowerconsumptionvaluesreportedin[7]:1.4Wfor
stayinsleepmodeexceptwhentheywakeupatthebeginning
transmission,1.0Wforreceiving,0.83Wforidling,and0.13W
of beacon periods. Each node also sends a 128-byte HELLO
for sleeping. We place 150 nodes uniformly at random on a
messageeverytwoseconds.Inthesecondscheme(No-PSM),
1000meterby1000metersquarearea.Thetransmissionrange
no power saving operation is used, and all nodes always stay
of each mobile node is 250 meters.
awakewithoutsendinganycontrolmessages.Wesendnodata
We choose 10 pairs of source and destination nodes uni-
traf(cid:2)c in either of the two reference cases.
formly at random among high-energy nodes; each source
In Figure 11 we present a snapshot for the number of
generatestraf(cid:2)c50secondsintothesimulationattheconstant
dead nodes over time. In this setting, approximately 30% of
rate of one 128-byte packet per second. The MAC-level
nodes are low-energy (L), 40% of them are medium-energy
transmission rate is 2 Mbps. As we discuss later, SPAN
(M), and the rest 30% are high-energy(H) nodes. (To denote
rotatesbackbonenodesfrequently(e.g.,2changespersecond),
this ratio, we use an abbreviated notation L:M:H=3:4:3.) In
which shortens path lifetimes. When we used on-demand
Figure11,thenetwork1-lifeofSPANissimilartothatof(cid:147)No-
routing protocols over SPAN, the path maintenance overhead
PSM.(cid:148)ThisisexpectedfromFigure10tosomeextent;SPAN
was high. Instead, we use an idealized scheme for packet
includeslow-energynodesinthebackbone,andtheirlifetimes
routing, where a path is found on top of the connected
decrease signi(cid:2)cantly. Although SPAN rotates the backbone
backboneusingthecentralizedFloyd-Warshallalgorithm[16]
node responsibility, there exists an unfortunate low-energy
implementedinns-2.Thiscorrespondstoabestcase scenario
node in most of our experiments that stays in the backbone
for SPAN. Nodes move according to the Random Waypoint
during the (cid:2)rst 350 seconds. In contrast, with TRUNC-1, the
mobility model (pause time=400s, and maximum speed is 1(cid:150)
network 1-life is close to 960 seconds, which is 2.7 times
16m/s) [21]. We also set the minimum speed to be 0.1m/s
longer than that of SPAN. This is because the TRUNC-1
to avoid speed decay [23]. Unless otherwise stated, we use
backbone consists mostly of high-energy nodes plus a few
mobile scenarios with the maximum speed of 1m/s.
medium-energynodes,andlow-energynodescanstayinsleep
In both TRUNC-1 and SPAN, each node sends a HELLO
message every two seconds. For TRUNC-1, we set the period 6We assume that the network needs external support after this time (e.g.,
of REQ messages to 14 seconds, which leads to reasonable addition offreshnodesinthecaseofsensornetworks).
10
Energyconsumption ratio(Idle:Sleep)
Ratioof 1-Life(sec) Half-Life(sec) 6.3:1[7] 14.0:1[25] 40.0:1[8]
L:M:H TRUNC-1 SPAN TRUNC-1 SPAN 1-life 152 189 220
4:4:2 892.1 365.5 1911.0 1506.3 half-life 24 34 43
(101.0) (28.3) (139.6) (54.5)
3:4:3 946.6 375.0 2106.2 1689.8 TABLEVII
(22.0) (29.1) (33.7) (40.5) LIFETIMEEXTENSIONINDIFFERENTENVIRONMENTS.
2:4:4 962.0 412.3 2208.3 1842.3
(13.7) (54.7) (41.1) (43.9) 1packet/sec 2packets/sec 4packets/sec
SPAN 0.96(0.04) 0.88(0.05) 0.62(0.02)
TABLEVI
TRUNC-1 0.98(0.02) 0.92(0.05) 0.58(0.04)
NETWORKLIFETIMESWITHVARIEDPROPORTIONOFNODESATDIFFERENT
TABLEVIII
ENERGYLEVELS.THEVALUESINPARENTHESESARESTANDARDDEVIATIONS.
AVERAGEDELIVERYRATIOWITHVARYINGTRAFFICLOAD.
modeandsaveenergy.Inthe case of TRUNC-1,we observea achieveslargernetworklifetimeextensionoverSPAN(e.g.,up
sharp increase in the number of dead nodes as the (cid:2)rst node to 220% increase in 1-lifetime, compared to previous 152%).
dies.Thisisthetime(960seconds)whenalllow-energynodes
Backbone Maintenance: We now examine the backbone
inTRUNC-1runoutofpower.Notethatthisisearlierthanthe
resilience as well as the effectiveness of our proposed main-
case of lower-bound (around 1050 seconds). This is because
tenancemechanismsagainstbackbonepartition.Let us de(cid:2)ne
with TRUNC-1, nodes consume more energy to exchange the coverage of a connected backbone to be the number
larger HELLO messages (in this experiment around 211 bytes
of nodes that are in the backbone or have a neighbor in
onaverage)thanthelower-boundcase(128bytes).Compared
the backbone. For an ideal connected backbone, its coverage
toSPAN,TRUNC-1alsoincreasestheaveragelifetimeoflow-
would always be equal to the number of nodes alive in the
energy nodes by 28% (1038.1 seconds vs. 811.3 seconds).
network. In Figure 12, we show the largest coverage of the
We now consider the lifetime of medium-energy nodes in TRUNC-1backboneovertime,whilewechangethemaximum
Figure 11. The use of low-energy backbone nodes in SPAN speed (1m/s, 8m/s, and 16m/s). Due to node mobility or
allows more medium-energy nodes to be in sleep mode and energy-level change, the backbone may get disconnected,
increasetheirlifetime.Still,comparedtoSPAN,theTRUNC-1 and we see occasional drops in the coverage of TRUNC-1
backbone increases the network half-life by around 26%. We backbone. However, our protocol detects such disconnections
explain this as follows. In this network setting, a connected quickly,andthelocalmaintenanceschemehelpstoregainthe
backboneneedstouseseveralmedium-energynodestomain- perfect coverage in a short period of time. As node mobility
tain connectivity. Ideally, as the initial medium-energy back- becomeshigher,weobservemodestincreaseinthenumberof
bonenodes expendtheir energy,theyshouldbe replacedwith partitionsintheTRUNC-1backbone.ComparedtotheTRUNC-
differentmedium-energynodes,suchthattheirlifetimesdonot 1 backbone, the SPAN backbone results in more frequent
decrease signi(cid:2)cantly. From Figure 11, we infer that TRUNC- coverage loss (Figure 13). In SPAN, nodes periodically leave
1 evenly distributes the backbone responsibility among all the backbone only after ensuring that the departure does not
medium-energynodes,andnomedium-energynodesdieuntil cause backbone disconnection. However, it is possible that a
1600 seconds. (In Figure 11, after all low-energy nodes die node makes such a decision based on outdated information
in the case of TRUNC-1 backbone, we observe a relatively (e.g., due to node mobility), which occurs frequently, for
stableperiodduringwhichnonodedies.)Incontrast,inSPAN, example, once every 30 seconds on average in Figure 13(a).
medium-energynodesstarttodiebefore1200seconds,andthe
Another aspect of backbone maintenance is the frequency
network half-life of SPAN decreased.
withwhichnodesinthebackbonechange.InFigure13(a),the
In Table VI, we tabulate the average network lifetimes and SPANbackboneundergoes674membershipchangesbetween
standard deviations while varying the proportion of nodes 100and400seconds.ThisisbecausebackbonenodesinSPAN
at different energy levels. We observe that in all scenarios, periodicallyleavethebackbone.Inthesamescenario,TRUNC-
TRUNC-1achieveslongernetworklifetimesthanSPAN(133(cid:150) 1 causes 49 changes in the backbone membership. Suppose
152% longer for 1-life and 20(cid:150)26% longer for half-life). We that an on-demand routing protocol such as DSR [1] found
also experimented using different parameters (e.g., different a path using backbone nodes. With SPAN, nodes on such a
initialbatterycapacityvaluesandL:M:Hratios),andTRUNC- path are likely to leave the backbone about 12 times more
1 outperformed SPAN in all cases. In all these experiments, frequently than TRUNC-1, and the source may need to (cid:2)nd a
the average backbone sizes of TRUNC-1 and SPAN are very newpathconsistingofbackbonenodesfrequently.(Recallthat
similar(between21and23nodesdependingonthescenarios). this is why we use the idealized routing in our experiments.)
In the previous experiments, we have used the energy Data Delivery: We brie(cid:3)y report the results about data
consumption values reported in [7]. In Table VII, we brie(cid:3)y delivery performance of TRUNC-1 backbone. In the previous
compare the results when we use different sets of values light-load experiments, both TRUNC-1 and SPAN achieve
reportedin [25] and[8].We onlyshow the ratio betweenidle near-perfect data delivery ratios. In this set of experiments
and sleep energy consumption, which is the most dominant we experimentwith high-loadscenarios using 1024-bytedata
difference between these sets. Compared to the results in Ta- packetswithvaryingpacketrates.Wealsousestaticnetworks
bleVI,asnodesinsleepmodeconsumelessenergy,TRUNC-1 andensurethedistancebetweensourceanddestinationismore