Compact Integer Programming Models for Power-optimal Trees in Ad Hoc Wireless Networks

Dag Haugland () and Di Yuan ()
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Dag Haugland: University of Bergen
Di Yuan: Linköping University

Chapter Chapter 10 in Wireless Network Design, 2011, pp 219-246 from Springer

Abstract: Abstract This chapter examines two types of optimization problems of minimizing the total transmission power required to satisfy some connectivity requirement for a group of nodes in ad hoc wireless networks. The first problem type is broadcast and multicast of messages from a source node to the rest of the group. The second problem type, also known as range assignment, amounts to forming a strongly connected subgraph containing all nodes of the group by bi-directional links. Optimal solutions to these problems are characterized by trees or arborescences. As a consequence of power minimization in a wireless transmission environment, the structural properties of these optimal trees and arborescences differ significantly from the classical ones. We discuss compact integer programming models for both problem types. In addition to reviewing models based on network flows, we develop a new compact model for range assignment. We provide theoretical analysis of how the models relate to each other in the strengths of their linear programming (LP) relaxations. Experimental results are provided to illustrate the performance of the models in bounding and in approaching integer optimality. The new compact model for range assignment turns out to be very competitive in both aspects.

Keywords: Wireless Network; Minimum Span Tree; Steiner Tree; Valid Inequality; Linear Programming Relaxation (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-1-4419-6111-2_10

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