 
Summary: Optimization Methods for Minimum Power
Bidirectional Topology Construction in Wireless
Networks with Sectored Antennas
Arindam K. Das, Robert J. Marks, Mohamed ElSharkawi, Payman Arabshahi, Andrew Gray
Abstract We consider the problem of minimum power bidi
rectional topology optimization in wireless networks with sectored
antennas. We first develop a mixed integer linear programming
model for optimal solution of the problem with sectored anten
nas. Subsequently, we discuss a centralized heuristic algorithm
which is based on Kruskal's algorithm for the minimum spanning
tree problem. However, unlike Kruskal's algorithm which chooses
minimum cost edges from a set of edge weights, our algorithm uses
an incremental cost mechanism to select edges. This incremental
cost mechanism is motivated by the inherently broadcast nature
of the wireless medium. We also discuss a simple branch exchange
heuristic which can be used to improve the topology generated by
the Kruskallike algorithm. Simulation results indicate that rea
sonably good solutions can be obtained using the proposed heuris
tic algorithms.
I. INTRODUCTION
