A theoretical Approach to Efficient Maximal/Minimal Enumeration Algorithm and its Applications

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Maximal (minimal) solutions are those not included in (not including) other solutions. Generally speaking, enumeration of maximal (minimal) solutions is not easy since they usually have no neighboring relations. In this research, we research efficient schemes of enumeration based on algorithmic technologies such as reverse search and the use of sparsity. As a result, we developed efficient enumeration algorithms for multi criteria optimization problem, perfect sequence, dense subgraph, ambiguous frequent itemset, and distance hereditary graphs.