A Branch and Bound Algorithm for Coalition Structure Generation over Graphs
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 NPcomplete. 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 intracoalitional 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.
 Publication:

arXiv eprints
 Pub Date:
 April 2020
 arXiv:
 arXiv:2004.13425
 Bibcode:
 2020arXiv200413425F
 Keywords:

 Computer Science  Computer Science and Game Theory
 EPrint:
 19 pages