Minimum power broadcast trees for wireless networks: integer programming formulations

Abstract

Abstract-Wireless multicast/broadcast sessions, unlike wired networks, inherently reaches several nodes with a single transmission. For omnidirectional wireless broadcast to a node, all nodes closer will also be reached. An algorithm for constructing the minimum power tree in wireless networks was first proposed by Wieselthier Ø Ð. The ÖÓ ×Ø Ò Ö Ñ ÒØ Ð ÔÓÛ Ö (BIP) algorithm suggested by them is a "node-based" minimum-cost tree algorithm for wireless networks. We propose an alternate search based paradigm wherein minimum-cost trees in wireless networks are found through a search process. Two computationally efficient procedures for checking the feasibility (viability) of a solution in the search space are presented. A straightforward procedure for initializing the search using stochastically generated trees is also proposed.

Exact algorithms for the minimum power symmetric connectivity problem in wireless networks

“…The mixed integer programming formulation described in this section is inspired by those presented in Das et al [4]. It is based based on a network flow model (see Magnanti and Wolsey [8]).…”

“…A branch and cut algorithm based on a new integer programming formulation is proposed in Althaus et al [1]. Some mixed integer programming formulations for an optimization problem similar to M P SC, where a host has to broadcast a message to all the other nodes, and the bidirectionality constraint for the links is relaxed, are presented in Das et al [4]. Different heuristic approaches for the same problem are proposed in Wieselthier et al [11], where some constructing algorithms are described, in Marks II et al [7], where an evolutionary approach using genetic algorithms is presented together with methods for generating initial solutions, and in Das et al [3], where an ant colony system approach is described.…”

A modified broadcast strategy for distributed signal estimation in a wireless sensor network with a tree topology

“…(15) where d kq is the distance between nodes k and q, and α > 2 is a constant [8,12] and b is the number of bits. We denote E kq,F as the energy required for a node k to reach its single neighbor to which a fusion flow signal is transmitted and bs represents the number of bits for signal transmission.…”

“…This signal fusion reduces the amount of bandwidth required for the transmission of each node's signal. Furthermore, in using a tree topology, each node needs only to communicate with nearby nodes which can reduce the transmission energy [8].…”

Iterated Local Optimization for Minimum Energy Broadcast

“…As an exact method to obtain globally optimal solutions, a mixed integer programming (IP) formulation for MINIMUM ENERGY BROADCAST has been presented by Das, et al [7]. Albeit valuable for theoretical reasons, its practical usage is limited to only small input sizes, as is the usual case for many IP problems.…”