Energy Efficient Broadcast in WANETs under an Overhearing Cost Model

1
Energy Efficient Broadcast in WANETs under an
Overhearing Cost Model

• Guofeng Deng
• IMPACT Lab at ASU

2
Outline

• Introduction
• Related work
• Network model
• Minimum energy broadcast (MinEB)
• Maximum lifetime broadcast (MaxLB)

3
Introduction

• Motivation
• Broadcast is an essential networking primitive
• Wireless broadcast medium
• Reception energy consumption matters, e.g., in
  TelosB, reception power is as much as peak
  transmission power
• Overhearing cost charged at each non-destination
  node, unless
• Fine-grained network synchronization, switching
  on/off related/unrelated nearby receivers
• Contributions include approximation algorithms to
  the following problems
• Minimum energy broadcast tree based on directed
  Steiner tree problem (DST)
• Maximum lifetime broadcast tree based on
  connected dominating neighbor problem (CDN)

4
Related Work

• Under simple reception energy cost model
• Maximum lifetime broadcast problem is simple
• Minimum energy broadcast problem is NP-hard and
  well studied connected dominating set (CDS)
• Minimum energy convergecast in WSN optimum
  branching problem Basu Redi, IPSN04
• Minimum energy broadcast w/o transmission power
  control connected exact cover (CEC) Lee Mans,
  VTC06
• Maximum lifetime broadcast greedy heuristic
  Deng Gupta, ICDCN06
• Interference aware broadcast somewhat related
  depending on definition of interference

5
Network Model

• Optimization problems
• Unit vs weighted cost (UC/WC)
• Undirected vs directed graph (UG/DG)
• Steiner vs spanning subgraph

• Transmission power
• Identical
• Adjustable in discrete levels
• Reception power
• Identical
• Non-identical
• Wireless medium
• Symmetric
• Asymmetric
• Battery capacity
• Identical
• Non-identical
• One-to-many traffic
• Broadcast
• Multicast

Approximate solutions
MinEB UC WC
UG Lee06
DG
MaxLB UC WC
UG ?
DG ? ?
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Minimum Energy Broadcast

• MinEB In a WANET, find a spanning tree rooted at
  the given source node such that the overall power
  consumption (OPC) is minimized.

An example Let node s be the source and energy
consumed for receiving each packet is 5 µJ for
each node equally. OPC(T1) (80) (10)
(75) 5 35 OPC(T2) (9) (5) (5) (5)
24
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Minimum Energy Broadcast (2)

• Convert the MinEB problem to the minimum directed
  Steiner tree (DST) problem
• In the widget Gv(Vv,Ev) of a node v, a square vr
  corresponds the receiving state and a hexagon vti
  corresponds to the state that the node is
  transmitting at its ith power level. An arch
  (vr,vti) is weighted as the sum of the
  transmission power at the ith level and the
  corresponding overhearing cost in the
  neighborhood.
• The inter-widget arch set Eint the is an arch
  (uti,vr) if v can receive the packet transmitted
  by u at its ith power level. For each arch in
  Eint, the weight is 0.
• A directed graph G(UVv, UEvUEint) that has
  n(p1) vertices and up to n2p arches, where n is
  the number of nodes in the original network and p
  is the number of power levels of eahc node.
• The best known DST approximation ratio is O(ke)
  for any fixed egt0, where k is the number of
  terminals Charikar et al., ACM-SIAM98
• This solution covers the cases of weighted cost
  and directed graph as well as multicast traffic.

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Maximum Lifetime Broadcast

• Discuss unit cost in undirected graph, the
  transmission power is ignored for now
• Transmission power control can make it fairly
  small compared to reception power
• Will be consider later
• MaxLB is essentially finding a subnetwork, in
  which the source node is connected to all the
  other nodes and the maximum number of
  transmitting neighbors of a node is minimized.
• Trivial greedy algorithm may have O(n)
  performance Deng Gupta, ICDCN06
• Convert the MaxLB problem to an optimization
  problem in a graph, which is the minimum
  connected dominating neighbor problem (CDN)

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CDN

• Problem In a graph G(V,E), find a connected
  dominating set D such that maxd(v) is
  minimized, where d(v) is the dominating degree
  defined as the number of neighbor nodes of v that
  belong to D.
• To convert MinLB to CDN, add a dummy node and
  connect it to the source node.

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CDN (2)

• CDN is NP-hard (reduce set cover to CDN)
• Related problems connected dominating set (CDS),
  minimum degree spanning tree (MDST), connected
  exact cover (CEC)

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CDN (3) Future work

• Algorithm update look-ahead greedy algorithm
  Guha Khuller, Algorithmica98
• Performance guarantee proof
• Extend to weighted cost and directed graph
• Extend to include transmission power