Power Optimization in Fault-Tolerant Topology Control Algorithms for Wireless Multi-hop Networks

• Published in: IEEE/ACM transactions on networking Vol. 15; no. 6; pp. 1345 - 1358
• Main Authors: Hajiaghayi, M.T., Immorlica, N., Mirrokni, V.S.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2007; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Ad hoc networks; Algorithm design and analysis; Algorithms; Approximation; Approximation algorithms; Attenuation; Connectivity; Control algorithms; Costs; Distributed algorithms; Energy consumption; Fault tolerance; graph model; graph properties; Graphs; Heuristic; Mathematical analysis; Network topology; Networks; Optimization; power conservation; Spread spectrum communication; Studies; topology control; Wireless communication; Wireless networks; Ad hoc networks; approximation algorithms; power conservation; topology control; graph properties; graph model
• ISSN: 1063-6692; 1558-2566
• DOI: 10.1109/TNET.2007.902680

In ad hoc wireless networks, it is crucial to minimize power consumption while maintaining key network properties. This work studies power assignments of wireless devices that minimize power while maintaining k-fault tolerance. Specifically, we require all links established by this power setting be symmetric and form a k-vertex connected subgraph of the network graph. This problem is known to be NP-hard. We show current heuristic approaches can use arbitrarily more power than the optimal solution. Hence, we seek approximation algorithms for this problem. We present three approximation algorithms. The first algorithm gives an O(kalpha)-approximation where is the best approximation factor for the related problem in wired networks (the best alpha so far is O(log k)). With a more careful analysis, we show our second (slightly more complicated) algorithm is an O(k)-approximation. Our third algorithm assumes that the edge lengths of the network graph form a metric. In this case, we present simple and practical distributed algorithms for the cases of 2- and 3-connectivity with constant approximation factors. We generalize this algorithm to obtain an O(k 2c+2 )-approximation for general k-connectivity (2 les c les 4 is the power attenuation exponent). Finally, we show that these approximation algorithms compare favorably with existing heuristics. We note that all algorithms presented in this paper can be used to minimize power while maintaining -edge connectivity with guaranteed approximation factors. Recently, different set of authors used the notion of k-connectivity and the results of this paper to deal with the fault-tolerance issues for static wireless network settings.