Optimal Design Of Wireless Ad-Hoc Networks

Abstract

This paper investigates the optimal design and deployment of wireless ad—hoc networks. Wireless ad—hoc networks are a new form of wireless communications that do not rely on any fixed infrastructure like wired base stations to keep the network up and running. Instead, hosts in a wireless ad—hoc network rely on each other to keep the network connected over either radio or infrared. Since direct communication is allowed only between adjacent nodes, distant nodes in an ad—hoc network communicate over multiple hops. We examine the optimal design of such networks by modeling the problem as a mixed integer mathematical program, and deriving solution procedures based on Lagrangean Relaxation (LR). Using the LR, we were able to decompose the network design problem into two fairly—easy—to—solve sub—problems. We present algorithms for each sub—problem, and an overall heuristic based on LR to solve the design problem. From the computational experiments we have done, our Lagrangean relaxation based algorithms can generate solutions within 2.20–13.16% of optimality. In addition, our algorithm also solves the design problem very rapidly, within a few minutes in the most complex case.