Novel algorithms for the network lifetime problem in wireless settings

Abstract

Abstract. A wireless ad-hoc network is a collection of transceivers positioned in the plane. Each transceiver is equipped with a limited, nonreplenishable 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. This problem is known to be NP-Hard for a variety of network operations. In this paper we are interested in two fundamental types of transmissions, broadcast and data gathering. We provide polynomial time approximation algorithms, with guaranteed performance bounds, for the maximum lifetime problem under two communication models, omnidirectional and unidirectional antennas. We also consider an extended variant of the maximum lifetime problem, which simultaneously satisfies additional constraints, such as bounded hop-diameter and degree of the routing tree, and minimizing the total energy used in a single transmission.

Improved Approximation Algorithms for Maximum Lifetime Problems in Wireless Networks

“…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 [6]. 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.…”

“…We observe that the problem is APX-hard, and the broadcast version is hard even for unit weights (however, Convergcast version with unit weights is polynomially solvable). In fact, for Broadcast, even determining whether k ≥ 1 is NP-complete [6]. Hence it seems that an approximation ratio of the type k/ρ is the best one can expect.…”

“…Hence it seems that an approximation ratio of the type k/ρ is the best one can expect. We give algorithms when ρ is a constant, improving the ratio ρ = O(log n) established in [6].…”

“…In these problems, every node v has a limited battery capacity b(v), and a transmission energy w(vu) to any other node u is known. In transmission round i, we choose a subnetwork H i with given properties, and every node transmits one message to each one of its neighbors in H i ; in many applications, each H i is an arborescence (see [6]). The goal is to maximize the lifetime of the network, that is to find a maximum length feasible sequence H 1 , H 2 , .…”

“…This is the Multiple Topology version of the problem. In the Single Topology variant, all the networks H i are identical, c.f., [6] for more details. We note that in [16] was given a constant ratio approximation algorithm for the case when each H i should be an st-path, for given s, t ∈ V .…”