Chapter

Discovery Science

Volume 3245 of the series Lecture Notes in Computer Science pp 32-46

Finding Optimal Pairs of Cooperative and Competing Patterns with Bounded Distance

  • Shunsuke InenagaAffiliated withCarnegie Mellon UniversityDepartment of Computer Science, University of Helsinki
  • , Hideo BannaiAffiliated withCarnegie Mellon UniversityHuman Genome Center, Institute of Medical Science, The University of Tokyo
  • , Heikki HyyröAffiliated withCarnegie Mellon UniversityPRESTO, Japan Science and Technology Agency (JST)
  • , Ayumi ShinoharaAffiliated withCarnegie Mellon UniversityPRESTO, Japan Science and Technology Agency (JST)Department of Informatics, Kyushu University 33
  • , Masayuki TakedaAffiliated withCarnegie Mellon UniversitySORST, Japan Science and Technology Agency (JST)Department of Informatics, Kyushu University 33
  • , Kenta NakaiAffiliated withCarnegie Mellon UniversityHuman Genome Center, Institute of Medical Science, The University of Tokyo
  • , Satoru MiyanoAffiliated withCarnegie Mellon UniversityHuman Genome Center, Institute of Medical Science, The University of Tokyo

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Abstract

We consider the problem of discovering the optimal pair of substring patterns with bounded distance α, from a given set S of strings. We study two kinds of pattern classes, one is in form \(p \land_\alpha q\) that are interpreted as cooperative patterns within α distance, and the other is in form \(p \land_\alpha \lnot q\) representing competing patterns, with respect to S. We show an efficient algorithm to find the optimal pair of patterns in O(N 2) time using O(N) space. We also present an O(m 2 N 2) time and O(m 2 N) space solution to a more difficult version of the optimal pattern pair discovery problem, where m denotes the number of strings in S.