Two fundamental algorithm-design paradigms are Tree Search and Dynamic Programming. The techniques used therein have been shown to complement one another when solving the complete set partitioning problem, also known as the coalition structure generation problem [5]. Inspired by this observation, we develop in this paper an algorithm to solve the coalition structure generation problem on graphs, where the goal is to identifying an optimal partition of a graph into connected subgraphs. More specifically, we develop a new depth-first search algorithm, and combine it with an existing dynamic programming algorithm due to [9]. The resulting hybrid algorithm is empirically shown to significantly outperform both its constituent parts when the subset-evaluation function happens to have certain intuitive properties.
The pseudo code of @math is shown in Algorithm . For a proof of the correctness of this algorithm, see @cite_1 .
@cite_1
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We present a new Dynamic Programming (DP) formulation of the Coalition Structure Generation (CSG) problem based on imposing a hierarchical organizational structure over the agents. We show the efficiency of this formulation by deriving DyPE, a new optimal DP algorithm which significantly outperforms current DP approaches in speed and memory usage. In the classic case, in which all coalitions are feasible, DyPE has half the memory requirements of other DP approaches. On graph-restricted CSG, in which feasibility is restricted by a (synergy) graph, DyPE has either the same or lower computational complexity depending on the underlying graph structure of the problem. Our empirical evaluation shows that DyPE outperforms the state-of-the-art DP approaches by several orders of magnitude in a large range of graph structures (e.g. for certain scalefree graphs DyPE reduces the memory requirements by @math and solves problems that previously needed hours in minutes).