Localized Algorithms for Energy Efficient Topology in Wireless Ad Hoc Networks

Topology control in wireless ad hoc networks is to select a subgraph of the communication graph (when all nodes use their maximum transmission range) with some properties for energy conservation. In this paper, we propose two novel localized topology control methods for homogeneous wireless ad hoc networks. Our first method constructs a structure with the following attractive properties: power efficient, bounded node degree, and planar. Its power stretch factor is at most , and each node only has to maintain at most neighbors where the integer is an adjustable parameter, and β is a real constant between 2 and 5 depending on the wireless transmission environment. It can be constructed and maintained locally and dynamically. Moreover, by assuming that the node ID and its position can be represented in bits each for a wireless network of n nodes, we show that the structure can be constructed using at most 24n messages, where each message is bits. Our second method improves the degree bound to k, relaxes the theoretical power spanning ratio to , where is an adjustable parameter, and keeps all other properties. We show that the second structure can be constructed using at most 3n messages, where each message has size of bits. We also experimentally evaluate the performance of these new energy efficient network topologies. The theoretical results are corroborated by the simulations: these structures are more efficient in practice, compared with other known structures used in wireless ad hoc networks and are easier to construct. In addition, the power assignment based on our new structures shows low energy cost and small interference at each wireless node. The work of Xiang-Yang Li is partially supported by NSFCCR-0311174. Wen-Zhan Song received Ph.D. from Illinois Institute of Technology in 2005, BS and MS from Nanjing University of Science and Technology in 1997 and 2000. He is currently an assistant professor in Washington State University. His current research interest is mainly focus on network protocol and algorithm design, especially in wireless networks, sensor networks and Peer-to-Peer networks. He is a member of the IEEE. Yu Wang received the Ph.D. degree in computer science from Illinois Institute of Technology in 2004, the BEng degree and the MEng degree in computer science from Tsinghua University, China, in 1998 and 2000. He has been an assistant professor of computer science at the Univeristy of North Carolina at Charlotte since 2004. His current research interests include wireless networks, mobile computing, algorithm design, and artificial intelligence. He is a member of the ACM, IEEE, and IEEE Communication Society. Xiang-Yang Li has been an Assistant Professor of Computer Science at the Illinois Institute of Technology since 2000. He hold MS (2000) and PhD (2001) degree at Computer Science from University of Illinois at Urbana-Champaign. He received his Bachelor degree at Computer Science and Bachelor degree at Business Management from Tsinghua University, P.R. China in 1995. His research interests span the computational geometry, wireless ad hoc networks, game theory, cryptography and network security. He is a Member of the ACM, IEEE, and IEEE Communication Society. Ophir Frieder is the IITRI Professor of Computer Science at the Illinois Institute of Technology. His research interests span the general area of distributed information systems. He is a Member of ACM and a Fellow of the IEEE.