Energy Efficient Broadcast in WANETs under an Overhearing Cost Model

Guofeng DengIMPACT Lab at ASU

Outline

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

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)

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, IPSN’04] Minimum energy broadcast w/o transmission power

control: connected exact cover (CEC) [Lee & Mans, VTC’06]

Maximum lifetime broadcast: greedy heuristic [Deng & Gupta, ICDCN’06]

Interference aware broadcast: somewhat related depending on definition of interference

Network Model

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

Optimization problems Unit vs weighted cost (UC/WC) Undirected vs directed graph

(UG/DG) Steiner vs spanning subgraph

MinEB UC WC

UG Lee’06

DG

MaxLB UC WC

UG ?

DG ? ?

Approximate solutions

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.

Tv

Rv

Tv ppTOPC )(

s a

b

c

5

6

9

7

8(A) Network

s a

b

c

5

7

8

(B) Tree T1

s a

b

c

5

9

8

(C) Tree T2

An example: Let node s be the source and energy consumed for receiving each packet is 5 µJ for each node equally.

OPC(T1) = (8+0) + (10) + (7+5) + 5 = 35

OPC(T2) = (9) + (5) + (5) + (5) = 24

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(p+1) 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(kε) for any fixed ε>0, where k is the number of terminals [Charikar et al., ACM-SIAM’98]

This solution covers the cases of weighted cost and directed graph as well as multicast traffic.

vr

vt1

vt1

vt1

The widget Gv=(Vv,Ev)

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, ICDCN’06]

Convert the MaxLB problem to an optimization problem in a graph, which is the minimum connected dominating neighbor problem (CDN)

CDN

Problem: In a graph G=(V,E), find a connected dominating set D such that max{δ(v)} is minimized, where δ(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.

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)

(A) graph G=(V,E) (B) Optimal CDS (C) Optimal CDNReduce set cover to CDN

CDN (3): Future work

Algorithm: update look-ahead greedy algorithm [Guha & Khuller, Algorithmica’98]

Performance guarantee proof Extend to weighted cost and directed

graph Extend to include transmission power