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STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
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CPM '01 Proceedings of the 12th Annual Symposium on Combinatorial Pattern Matching
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CloseGraph: mining closed frequent graph patterns
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
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CPM'03 Proceedings of the 14th annual conference on Combinatorial pattern matching
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ILP'05 Proceedings of the 15th international conference on Inductive Logic Programming
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Maximal and minimal representations of gapped and non-gapped motifs of a string
Theoretical Computer Science
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DS '09 Proceedings of the 12th International Conference on Discovery Science
Time and space efficient discovery of maximal geometric graphs
DS'07 Proceedings of the 10th international conference on Discovery science
Mining maximal flexible patterns in a sequence
JSAI'07 Proceedings of the 2007 conference on New frontiers in artificial intelligence
Mining frequent k-partite episodes from event sequences
JSAI-isAI'09 Proceedings of the 2009 international conference on New frontiers in artificial intelligence
Structural analysis of gapped motifs of a string
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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In this paper, we consider the problem of enumerating all maximal motifs in an input string for the class of repeated motifs with wild cards. A maximal motif is such a representative motif that is not properly contained in any larger motifs with the same location lists. Although the enumeration problem for maximal motifs with wild cards has been studied in (Parida et al., CPM'01), (Pisanti et al.,MFCS'03) and (Pelfrene et al., CPM'03), its output-polynomial time computability is still open. The main result of this paper is a polynomial space polynomial delay algorithm for the maximal motif enumeration problem for the repeated motifs with wild cards. This algorithm enumerates all maximal motifs in an input string of length n with O(n3) time per motif with O(n2) space and O(n3) delay. The key of the algorithm is depth-first search on a tree-shaped search route over all maximal motifs based on a technique called prefix-preserving closure extension. We also show an exponential lowerbound and a succinctness result on the number of maximal motifs, which indicate the limit of a straightforward approach.