Optimization in wireless networks: lifetime, relay, and broadcast schedules

In this dissertation, four optimization problems in wireless networks are explored. The first two are to compute a schedule to maximize the sensor network lifetime which is measured by total time during which the network performs its monitoring duties without recharging batteries. First, considering the wireless sensor networks where sensors are assumed to be on all the time, the previously proposed exact polynomial-time algorithm has O(n15logn) running time. We demonstrate an alternative approach giving a solution at least 1 – e times the optimum lifetime, with running time O(n3 1e 7 log1+e n), for any e > 0. Second, assuming a sensor network model in which sensors can interchange idle and active statuses both for monitoring and communicating, we propose centralized approximation algorithms for lifetime maximization. Also, a distributed Deterministic Energy-Efficient Protocol for Sensing (DEEPS) to prolong lifetime is proposed. The experimental results reveal an increase in the lifetime for DEEPS over known protocols. Third, we study the problem of Relay Nodes in Wireless Sensor Networks. Given a set S of wireless sensor nodes as a set of points in the two-dimensional plane, we must place a minimum-size set Q of relay nodes to connect S. The nodes of S can communicate to nodes within distance r and the relay nodes of Q can communicate within distance R. We improve the analysis of the 7-approximation algorithm based on Minimum Spanning Tree (MST) to 6 and propose a post-processing heuristic to improve the performance of the approximation algorithms. Fourth, we study the Interference-Aware Broadcast Scheduling problem, where all nodes in the Euclidean plane have a transmission range and an interference range equal to r and stir for αr ≥ 1, respectively. Minimizing latency is known to be NP-hard even when α = 1. We present integer programs for the problem and compare the optimum solution to that obtained from our newly proposed heuristics. The experiments reveal that our best heuristics give the solutions 13-20% exceeding the optimums. We additionally demonstrate that an O (αD) schedule exists and therefore O (α) approximation algorithm is attained.