Abstract The space of coalition structure is abstracted as a coalition structure graph, and two operators, union and intersection, are defined. Thus, all the coalition structures form an algebra structure, coalition structure lattice (CSL). In order to simplify the study of CSL algebra property, the integer split graph is introduced, and a mapping relation F from coalition structures to integer splits and an equivalent relation EF based on F are constructed. Therefore, during searching optimal coalition structure in CSL, the current optimal value and average value are used as prune function. When the upper bound of some equivalent class is lower than the prune function, a large number of coalition structures in equivalent class are pruned. Finally, better dynamic programming (BDP) algorithm is given, and the validity of the proposed algorithm is proved by experimental analysis. Furthermore, the results indicate that BDP decreases 43% searching numbers than dynamic programming when there are 20 agents.
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