Wireless Network Design: Optimization Models and Solution ...

Chapter 10
Compact Integer Programming Models for
Power-optimal Trees in Ad Hoc Wireless
Networks
Dag Haugland and Di Yuan
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.
10.1 Introduction
Power efficiency is a key aspect in many applications of ad hoc wireless networks,
where the networking devices set up a self-organizing communication environment
without pre-installed infrastructure (cf. mobile cellular networks). Two devices in ad
Dag Haugland
Department of Informatics, University of Bergen, PB. 7800, N-5020 Bergen, Norway, e-mail:
Dag.Haugland@ii.uib.no
Di Yuan
Department of Science and Technology, Linköping University, SE-601 74 Norrköping, Sweden,
e-mail: diyua@itn.liu.se
J. Kennington et al. (eds.), Wireless Network Design: Optimization Models and Solution
Procedures, International Series in Operations Research and Management Science 158,
DOI 10.1007/978-1-4419-6111-2_10, © Springer Science+Business Media, LLC 2011
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