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Coalition formation typically involves the coming together of multiple,heterogeneous, agents to achieve both their individual and collective goals. Inthis paper, we focus on a special case of coalition formation known asGraph-Constrained Coalition Formation (GCCF) whereby a network connecting theagents constrains the formation of coalitions. We focus on this type of problemgiven that in many real-world applications, agents may be connected by acommunication network or only trust certain peers in their social network. Wepropose a novel representation of this problem based on the concept of edgecontraction, which allows us to model the search space induced by the GCCFproblem as a rooted tree. Then, we propose an anytime solution algorithm(CFSS), which is particularly efficient when applied to a general class ofcharacteristic functions called $m+a$ functions. Moreover, we show how CFSS canbe efficiently parallelised to solve GCCF using a non-redundant partition ofthe search space. We benchmark CFSS on both synthetic and realistic scenarios,using a real-world dataset consisting of the energy consumption of a largenumber of households in the UK. Our results show that, in the best case, theserial version of CFSS is 4 orders of magnitude faster than the state of theart, while the parallel version is 9.44 times faster than the serial version ona 12-core machine. Moreover, CFSS is the first approach to provide anytimeapproximate solutions with quality guarantees for very large systems of agents(i.e., with more than 2700 agents).

Algorithms for Graph-Constrained Coalition Formation in the Real World