Minimum-energy broadcast and multicast in wireless networks: An integer programming approach and improved heuristic algorithms

Abstract

Both integer programming models and heuristic algorithms have been proposed for finding minimum-energy broadcast and multicast trees in wireless ad hoc networks. Among heuristic algorithms, the broadcast/multicast incremental power (BIP/MIP) algorithm is most known. The theoretical performance of BIP/MIP has been quantified in several studies. To assess the empirical performance of BIP/MIP and other heuristic algorithms, it is necessary to compute an optimal tree or a very good lower bound of the optimum. In this paper we present an integer programming approach as well as improved heuristic algorithms. Our integer programming approach comprises a novel integer model and a relaxation scheme. Unlike previously proposed models, the continuous relaxation of our model leads to a very sharp lower bound of the optimum. Our relaxation scheme allows for performance evaluation of heuristics without having to compute optimal trees. Our contributions to heuristic algorithms consist of the power-improving algorithm successive power adjustment (SPA), and improved time complexity of some previously suggested algorithms. We report extensive numerical experiments. Algorithm SPA finds better solutions in comparison to a host of other algorithms. Moreover, the integer programming approach shows that trees found by algorithm SPA are optimal or near-optimal.

A fast local search method for minimum energy broadcast in wireless ad hoc networks

“…For performing sweep exhaustively, we are not aware of any stronger time complexity results than the O(|V | 4 ) bound proved in [9]. This is in contrast to arborescence construction heuristics with low time complexity like BIP (O(|A| + |V | log |V |), [1]).…”

“…Most other suggested improvement heuristics (e.g. [4], [7], and [9]) do not perform exhaustive search. They rather execute a pre-defined number of search moves in order to be able to prove a certain time complexity (in general, O(|V | 3 )), or simply adopt a maximum time limit.…”

“…In [8], the local search heuristic sweep was introduced. For networks consisting of 20 nodes, applying sweep to an arborescence constructed by the well-known Broadcast Incremental Power (BIP) algorithm [8], for example, reduces the total power consumption from about 1.3 to about 1.17 times the optimal power consumption [9].…”

Dual Decomposition for Computational Optimization of Minimum-Power Shared Broadcast Tree in Wireless Networks

“…Among them, the most cited one is the broadcast incremental power (BIP) algorithm that is an adaptation of Prim's MST algorithm to MEB. The NP-hardness of MEB was established in [8], and the MEB literature is rich on studies of approximation algorithms [10,15,16,17,18,19,20,21] and heuristic algorithms [19,22,23,24,25,26,27]. Integer programming formulations were first presented in [7], and more recently in [27,28,29].…”

“…The authors of [4] presented integer programming and dynamic programming techniques for MEB with a hop limit. For minimumenergy multicast, research results are provided in [1,9,14,26,27,28].…”