Post on 29-Jan-2016
description
Mario Čagalj
joint work with Jean-Pierre Hubaux and Christian Enz
Minimum-Energy Broadcast in All-Wireless Networks:
NP-Completeness and Distribution Issues
2
Numerous sensor devices equipped with
Modest wireless communication, processing, and memory capabilitiesForm ad hoc network (self-organized)Low mobility (static)
Distributed systemBroadcasting - important communication primitive
Wireless Sensor Networks
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Find a minimum-energy broadcast tree
Design goals
j
i
l
o
m
n
kp
Minimize power consumption per packet
pjpk
pi
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Wireless Multicast Advantage (WMA) [WieselthierNE00]
Nodes equipped with omnidirectional antennas
i transmits at and reaches both j and k
Energy expenditure
j
Peculiarities of wireless media
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k
pik
pij
},max{ ikij pp},max{ ikijtot ppp
Wireless media is a node-based environment
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Graph
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ipc
Node-based network model
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),( EVG vip
s.t. are said to be covered by node
Captures the WMA property
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m
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Formal problem definition
Minimum Broadcast Cover (MBC) problemGiven , , edge costs , the source and an assignment
Find a power assignment vector s.t. it induces graph , , in which there is a path from r to any node of V, and . is minimized
Special case: Geometric MBC (GMBC) MBC in two-dimensional Euclidean metric space
Edge costs are given by
),( EVG P R)(: GEcijVr PGVp v
i )(:][ 21
vV
vv ppp ),( '' EVG }:),{(' v
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vip
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COROLLARY 1. MBC cannot be approximate better than O(log ) if P NP.
SC to MBC transformation preserves approximation ratio achievable for SCNo polynomial-time algorithm approximates SC better than O(log ) if P NP [D.S. Hochbaum]
Complexity issuesTHEOREM 1. Minimum Broadcast Cover (MBC) is NP-complete.
Set Cover (SC) is NP-complete [M. Garey and D. Johnson]MBCNP and SC MBC ( - polynomial transformation)
THEOREM 2. Geometric MBC (GMBC) is NP-complete.
Planar 3-SAT (P3SAT) is NP-complete [M. Garey and D. Johnson]GMBCNP and P3SAT GMBC
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Broadcast Incremental Power (BIP) [WieselthierNE00]
pb=8
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2
pa=2
Heuristics based approach
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pc=55
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5pe=4
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pd=4
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Embedded Wireless Multicast Advantage (EWMA)Begin with an initial feasible solution (minimum spanning tree)
Improve the initial solution by embedding the WMA property while preserving the feasibility of the solution
[WanCLF01])(12)( OPTpBIPp tottot
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EWMA by example (1/2),α
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Calculate gains6 d
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Calculate new transmission power
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pa=2
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pc=55
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pd=4
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EWMA by example (2/2)
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pa=13
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)()(
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MSTpBIPp tottot
[WanCLF01])(12)( OPTpMSTp tottot )(12)()( OPTpMSTpEWMAp tottottot
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Phase 1: Distributed-MST [GallagerHS83]
Distributed EWMA (1/2)
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Node x waits before it potentially becomes a forwarder x
wT
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egge
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if xw
Phase 2: Local EWMA
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Distributed EWMA (2/2)Lack of global information
Propagate information about forwarding nodes along the transmission chainPhase 2 organized in rounds of duration Probation , correction and active periods
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maxTcorrT actTprobT
probT corrT actT t
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Performance evaluationSimulation setup
100 instances x 10,30,50,100-nodes networks
Spatial Poisson distribution of nodes
Cost of links
The performance metric is a normalized power For k-nodes network
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Performance evaluation (1/2) Avg. Normalized Power vs. Network Size
= 4 = 3
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Performance evaluation (2/2)Avg. Normalized Power vs. Network Size
= 2 = 2
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ConclusionAchievements
Proved that building the minimum-energy broadcast tree in wireless networks is NP-complete
Devised a new algorithm:Embedded Wireless Multicast Advantage (EWMA)
Shown that it can be distributed
Future work Extend the network model (i.e. mobility, interference)
Take into account the battery lifetime
Consider the minimum-energy multicast problem
http://www.terminodes.org
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Synchronization of DEWMA
Necessary conditions
Duration of the second phase is bounded by
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