Improved approximation algorithms for maximum lifetime problems in wireless networks

A wireless ad-hoc network is a collection of transceivers positioned in the plane. Each transceiver is equipped with a limited battery charge. The battery charge is then reduced after each transmission, depending on the transmission distance. One of the major problems in wireless network design is to route network traffic efficiently so as to maximize the network lifetime, i.e., the number of successful transmissions. In this paper we consider Rooted Maximum Lifetime Broadcast/Convergecast problems in wireless settings. The instance consists of a directed graph G = (V,E) with edge-weights {w(e) : e ∈ E}, node capacities {b(υ) : υ ∈ V}, and a root r. The goal is to find a maximum size collection {T ₁, ..., T _k } of Broadcast/Convergecast trees rooted at r so that ∑_i=1^k w(δ_Ti(υ)) ≤ b (υ),, where δ _T (υ) is the set of edges leaving υ in T. In the Single Topology version all the Broadcast/Convergecast trees T _i are identical. We present a number of polynomial time algorithms giving constant ratio approximation for various broadcast and convergecast problems, improving previously known result of Ω(⌊1/log n ⌋)-approximation by [1]. We also consider a generalized Rooted Maximum Lifetime Mixedcast problem, where we are also given an integer γ≥ 0, and the goal is to find the maximum integer k so that k Broadcast and γk Convergecast rounds can be performed.