Competitive call control in mobile networks

Abstract

In this paper, we deal with competitive local on-line algorithms for non-preemptive channel allocation in mobile networks. The signal interferences in a network are modeled using an interference graph G. We prove that the greedy on-line algorithm is Δ-competitive, where Δ is the maximum degree of G. We employ the “classify and randomly select” paradigm ([5, 12]), and give a 5-competitive randomized algorithm for the case of planar interference graphs. We show that the problem of call control in mobile networks with multiple available frequencies reduces to the problem of call control in networks with a single frequency. Using this reduction, we present on-line algorithms for general networks with a single frequency. We give a local on-line algorithm which is \(\frac{{\alpha (\delta + 1 + \alpha )}}{{(1/2 + \alpha )^2 }}\)-competitive, where a is the independence number of G and δ is the average degree of G. The above results hold in the case that the duration of each request is infinite, and the benefit the algorithm gains by accepting each request is equal to 1. They are extended to handle requests of arbitrary durations, and arbitrary benefits. To our knowledge, this is the first time that competitive analysis is employed to study on-line algorithms for the channel allocation problem in mobile networks.