AAAI Publications, Thirty-First AAAI Conference on Artificial Intelligence

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Dancing with Decision Diagrams: A Combined Approach to Exact Cover
Masaaki Nishino, Norihito Yasuda, Shin-ichi Minato, Masaaki Nagata

Last modified: 2017-02-12


Exact cover is the problem of finding subfamilies, S*, of a family of sets, S, over universe U, where S* forms a partition of U.  It is a popular NP-hard problem appearing in a wide range of computer science studies. Knuth's algorithm DLX, a backtracking-based depth-first search implemented with the data structure called dancing links, is known as state-of-the-art for finding all exact covers. We propose a method to accelerate DLX. Our method constructs a Zero-suppressed Binary Decision Diagram (ZDD) that represents the set of solutions while running depth-first search in DLX. Constructing ZDDs enables the efficient use of memo cache to speed up the search. Moreover, our method has a virtue that it outputs ZDDs; we can perform several useful operations with them. Experiments confirm that the proposed method is up to several orders of magnitude faster than DLX.


Exact Cover; Dancing Links; Enumeration; Zero-suppressed Binary Decision Diagrams

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