Coalition Structure Generation on Graphs

Abstract: 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 Vinyals et al. [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.