Approximation Bounds on the Number of Mixedcast Rounds in Wireless Ad-Hoc Networks

Abstract

We consider the following type of Maximum Network Lifetime problems. For a wireless network N with given capacities of node batteries, and a specification of a communication task which is to be performed periodically in N, find a maximum-size feasible collection of routing topologies for this task. Such a collection of routing topologies defines the maximum number of rounds this task can be performed before the first node in the network dies due to battery depletion. The types of communication tasks which we consider are unicast, broadcast, convergecast and mixedcast. The mixedcast is the requirement that some fixed number of tasks of the basic types (unicast, broadcast, convergecast) are periodically performed. We show that one can compute in polynomial time the number k of mixedcast rounds which is at least $\lfloor{k_{opt}/5}\rfloor$, for the single-topology variant of the problem, and at least $\lfloor{k_{opt}/6}\rfloor$, for the multiple-topology variant, improving the previous bounds.

Research partially supported by the EPSRC grant EP/J006300/1 ”Random walks on computer networks” and the 2012 SAMSUNG GRO project “Fast Low Cost Methods to Learn Structure of Large Networks.”