Issues in ad hoc wireless networks

This thesis provides algorithms to solve several problems related to resource-efficient routing in ad hoc wireless networks and power-aware connectivity maintenance in wireless sensor networks. Recent research shows that with the introduction of a virtual backbone which is in charge of control packets dissemination, routing protocol overhead in ad hoc wireless networks can be effectively decreased. In this thesis, I first propose two distributed time/message efficient approximation algorithms to compute the virtual backbone. Both algorithms have linear message complexities. Algorithm I is cost-aware, which accommodates the strict network resources. Algorithm II is degree-aware, which generates the best result in literature so far to our knowledge. Simulation results and theoretical analysis show that both algorithms perform well. In this study, the virtual backbone is approximated by a “minimum connected dominating set (MCDS)” in unit-disk graphs. This is a NP-Hard problem. Other than the two efficient heuristics mentioned above, We also design a Polynomial Time Approximation Scheme (PTAS) for MCDS in unit-disk graphs. This tells that theoretically MCDS in unit-disk graphs can be approximated to any degree. Broadcast in ad hoc wireless networks is another challenging problem. We propose a heuristic to construct a broadcast tree rooted at the source. This broadcast tree has two features: it contains as many leaves as possible; and it favors hosts with lower cost. These features not only improve the broadcast efficiency but also balance routing burden in the whole network. Finally we propose a novel idea of maintaining connectivity by introducing relay sensors in wireless sensor networks. We formulate the problem to the NP-hard network optimization problem named Steiner Minimum Tree with Minimum number of Steiner Points (SMT-MSP) and present two approximate solutions. We also study the topology improvement by simulation when one or more relay sensors are introduced. The performance parameters under consideration include P, the total per node minimum power needed to maintain connectivity, and D, the maximum degree in the topology maintained by P. Simulation study shows that with the introduction of relay sensors, we achieve better performance, especially for sparse topology.