A Branch and Bound Algorithm for Coalition Structure Generation over Graphs

TL;DR

This paper introduces a branch and bound algorithm based on column generation for coalition structure generation over graphs, addressing NP-complete cases with experimental results on large agent sets.

Contribution

It presents a novel algorithm for coalition structure generation over graphs with new experimental validation on large-scale instances.

Findings

Successfully handled sets of more than forty agents.

Demonstrated effectiveness for valuation functions based on edge weights.

Provided theoretical analysis for coordination valuation.

Abstract

We give a column generation based branch and bound algorithm for coalition structure generation over graphs problem using valuation functions for which this problem is proven to be NP-complete. For a given graph G = (V;E) and a valuation function w : 2^V -> R, the problem is to find the most valuable coalition structure (or partition) of V. We consider two cases: first when the value of a coalition is the sum of the weights of its edges which can be positive or negative, second when the value of a coalition takes account of both inter- and intra-coalitional disagreements and agreements, respectively. For both valuations we give experimental results which cover for the first time sets of more than forty agents. For another valuation function (coordination) we give only the theoretical considerations in the appendix.