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, 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

5. 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 MinEBUCWC UGLee’06 DG MaxLBUCWC UG? DG?? Approximate solutions

6. 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) = (8+0) + (10) + (7+5) + 5 = 35 OPC(T2) = (9) + (5) + (5) + (5) = 24

7. Minimum Energy Broadcast (2) Convert the MinEB problem to the minimum directed Steiner tree (DST) problem  In the widget G v =(V v,E v ) of a node v, a square v r corresponds the receiving state and a hexagon v t i corresponds to the state that the node is transmitting at its i th power level. An arch (v r,v t i ) is weighted as the sum of the transmission power at the i th level and the corresponding overhearing cost in the neighborhood.  The inter-widget arch set E int : the is an arch (u t i,v r ) if v can receive the packet transmitted by u at its i th power level. For each arch in E int, the weight is 0.  A directed graph G=( U V v, U E v U E int ) that has n(p+1) vertices and up to n 2 p 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(k ε ) 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.

8. 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)

9. 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.

10. 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)

11. 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