A derivative structure is a nonequivalent substitutional atomic configuration derived from a given primitive cell. The enumeration of derivative structures plays an essential role in searching for the ground states in multicomponent systems. However, it is computationally difficult to enumerate derivative structures if the number of derivative structures of a target system becomes huge. In this study, we introduce a novel compact data structure of the zero-suppressed binary decision diagram (ZDD) for enumerating derivative structures much more efficiently. We show its simple applications to the enumeration of structures derived from the face-centered cubic and hexagonal close-packed lattices in binary, ternary, and quaternary systems. The present ZDD-based procedure should contribute to computational approaches based on derivative structures in physics and materials science.

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The maximum number of sites for the previous method is underestimated due to an internal problem of ENUMLIB in enumerating derivative structures for large indices. However, the underestimation is not essential in comparing the maximum numbers of sites. The maximum numbers of sites for the previous method, estimated by extrapolating the relationship between the index and the required peak memory, are 32, 22, and 17 for binary, ternary, and quaternary systems, respectively, which are also much smaller than those for the present ZDD-based method.

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