Maximum-lifetime routing algorithms for networks with omnidirectional and directional antennas

Abstract

A major problem in wireless networks is how to route either broadcast, unicast or multicast traffic so as to maximize the lifetime, i.e., the time until the battery of a transmitting node drains out. Focusing on the fundamental single-session problem, our solution approach is based on the employment of multi-topology routing schemes. Such a scheme consists of a set of routing topologies, which are employed sequentially, for some prescribed duration times.First, we consider the standard wireless environment of multiple recipients, which correspond to omnidirectional antennas. For the cases of either single-topology schemes or unicast sessions, we establish optimal solutions of polynomial complexity. For the general (multi-topology) cases of broadcast and multicast, which are NP-hard, we derive a novel heuristic scheme, and demonstrate its efficiency by way of simulations.We then consider an alternative, single-recipient wireless environment, which corresponds to the important case of directional antennas. While the employment of directional antennas is known to posses significant advantages over the traditional omnidirectional transmission, the problem of lifetime maximization under this environment has received only limited attention. We demonstrate that the change from the traditional (multiple-recipients) environment to the singlerecipient environment is of major significance in terms of computational complexity and produces an interesting twist of difficulty: namely, for the standard model, the singletopology broadcast problem is computationally solvable and the multi-topology problem is NP-hard, while the opposite holds for the single-recipient model. Finally, we discuss the extension of our results to the case of multiple sessions.

Novel algorithms for the network lifetime problem in wireless settings

“…Omnidirectional Model Orda and Yassour [5] gave polynomial-time algorithms for broadcast, multicast and unicast in the case of single source/single topology, which improved previous results by [6]. Segal [7] improved the running time of the MLB problem for the broadcast protocol and also showed an optimal polynomial-time algorithm for convergecast with aggregation.…”

“…By allowing single source/multiple topology, the broadcast and multicast become NP-Hard [5], while convergecast and unicast have polynomial-time optimal solutions. In [5], the authors establish an O(log n) and O(k ε ) approximation algorithms for broadcast and multicast, respectively, where k is the size of the multicast destination set and ε is any positive constant. The same paper shows an optimal solution for the unicast case by using linear programming and max-flow algorithms.…”

“…They also propose several heuristics and evaluate their performance by simulation. OPT [5] OPT [10] Generally, a common approach to solving the fractional problem is to use various LP formulations that reduce the problem to one of finding the maximum multicommodity flow in a network. See also [13][14][15].…”

“…Unidirectional Model The authors in [5] show that for broadcast, the problem is NP-Hard in the case of single source/single topology and has a polynomial solution in the case of single source/multiple topology. They also show that it is NP-Hard in both of these cases for multicast.…”

Improved Approximation Algorithms for Maximum Lifetime Problems in Wireless Networks

“…The authors in [17] show that for Broadcast, the problem is NP-Hard in the case of Single Source/Single Topology and has a polynomial solution for fractional version in the case of Single Source/Multiple Topology. They also show that it is NP-Hard in both of these cases for multicast.…”