Pre-processing Techniques for Anytime Coalition Structure Generation Algorithms

Abstract

This paper is concerned with optimal coalition structure generation in multi-agent systems. For characteristic function game representations, we propose pre-processing techniques, presented in the form of filter rules, that reduce the intractability of the coalition structure generation problem by identifying coalitions which cannot belong to any optimal structure. These filter rules can be incorporated into many potential anytime coalition structure generation algorithms but we test the effectiveness of these filter rules in the sequential application of the distributed coalition value calculation algorithm (DCVC) [1] and the anytime coalition structure generation algorithm of Rahwan et al. (RCSG) [2]. The distributed DCVC algorithm provides an input to the centralised RCSG algorithm and we show that, for both normal and uniform distributions of coalition values, the proposed filter rules reduce the size of this input by a considerable amount. For example, in a system of 20 agents, fewer than 5% of all coalition values have to be input, compared to more than 90% when filter rules are not employed. Furthermore, for a normal distribution of coalition values, the running time of the RCSG algorithm exponentially accelerates as a consequence of the significantly reduced input size. This pre-processing technique bridges the gap between the distributed DCVC and centralised RCSG algorithms and is a natural benchmark to develop a distributed CSG algorithm.