Algorithmic Aspects of Energy-Delay Tradeoff in Multihop Cooperative Wireless Networks

TL;DR

This paper investigates energy-efficient transmission strategies in delay-constrained cooperative multihop wireless networks, analyzing algorithmic complexity, proposing a generalized optimization framework, and empirically evaluating trade-offs between delay and power efficiency.

Contribution

It introduces a unified algorithmic formulation for cooperative schemes, proves NP-hardness and inapproximability results, and offers polynomial-time solutions for specific cases like unicast with energy accumulation.

Findings

The broadcast and multicast problems are NP-hard and hard to approximate.

A polynomial-time algorithm optimally solves joint power control and scheduling given an ordering.

Empirical results show near-optimal performance using heuristic orderings in typical scenarios.

Abstract

We consider the problem of energy-efficient transmission in delay constrained cooperative multihop wireless networks. The combinatorial nature of cooperative multihop schemes makes it difficult to design efficient polynomial-time algorithms for deciding which nodes should take part in cooperation, and when and with what power they should transmit. In this work, we tackle this problem in memoryless networks with or without delay constraints, i.e., quality of service guarantee. We analyze a wide class of setups, including unicast, multicast, and broadcast, and two main cooperative approaches, namely: energy accumulation (EA) and mutual information accumulation (MIA). We provide a generalized algorithmic formulation of the problem that encompasses all those cases. We investigate the similarities and differences of EA and MIA in our generalized formulation. We prove that the broadcast and multicast problems are, in general, not only NP hard but also o(log(n)) inapproximable. We break these problems into three parts: ordering, scheduling and power control, and propose a novel algorithm that, given an ordering, can optimally solve the joint power allocation and scheduling problems simultaneously in polynomial time. We further show empirically that this algorithm used in conjunction with an ordering derived heuristically using the Dijkstra's shortest path algorithm yields near-optimal performance in typical settings. For the unicast case, we prove that although the problem remains NP hard with MIA, it can be solved optimally and in polynomial time when EA is used. We further use our algorithm to study numerically the trade-off between delay and power-efficiency in cooperative broadcast and compare the performance of EA vs MIA as well as the performance of our cooperative algorithm with a smart noncooperative algorithm in a broadcast setting.