Forming effective coalitions is a major research challenge in AI and multi-agent systems. Coalition Structure Generation (CSG) involves partitioning a set of agents into coalitions so that social surplus (the sum of the rewards of all coalitions) is maximized. A partition is called a coalition structure (CS). In traditional works, the value of a coalition is given by a black box function called a characteristic function. In this paper, we propose a novel formalization of CSG, i.e., we assume that the value of a characteristic function is given by an optimal solution of a distributed constraint optimization problem (DCOP) among the agents of a coalition. A DCOP is a popular approach for modeling cooperative agents, since it is quite general and can formalize various application problems in MAS. At first glance, this approach sounds like a very bad idea considering the computational costs, since we need to solve an NP-hard problem just to obtain the value of a single coalition. To optimally solve a CSG, we might need to solve O(2
n) DCOP problem instances, where n is the number of agents. However, quite surprisingly, we show that an approximation algorithm, whose computational cost is about the same as solving just one DCOP, can find a CS whose social surplus is at least max(2/n, 1/(w
*+1)) of the optimal CS, where w
* is the tree width of a constraint graph. Furthermore, we can generalize this approximation algorithm with a parameter k, i.e., the generalized algorithm can find a CS whose social surplus is at least max(2k/n, k/(w
*+1)) of the optimal CS by
exploring
more search
space
. These results illustrate that the locality of interactions among agents, which is explicitly modeled in the DCOP formalization, is quite useful in developing efficient CSG algorithms with quality guarantees.
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