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Fast Algorithms for Finding Maximum-Density Segments of a Sequence with Applications to Bioinformatics

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Book cover Algorithms in Bioinformatics (WABI 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2452))

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Abstract

We study an abstract optimization problem arising from biomolecular sequence analysis. For a sequence A = 〈a 1, a 2, ..., a n〉 of real numbers, a segment S is a consecutive subsequence 〈a i, a i+1, ..., a j〉. The width of S is j - i + 1, while the density is (∑i≤k≤j a k)/(j - i+1). The maximum-density segment problem takes A and two integers L and U as input and asks for a segment of A with the largest possible density among those of width at least L and at most U. If U = n (or equivalently, U = 2L - 1), we can solve the problem in O(n) time, improving upon the O(n log L)-time algorithm by Lin, Jiang and Chao for a general sequence A. Furthermore, if U and L are arbitrary, we solve the problem in O(n + n log(U - L + 1)) time. There has been no nontrivial result for this case previously. Both results also hold for a weighted variant of the maximum-density segment problem.

Supported in part by NSF grant EIA-0112934.

Supported in part by NSC grant NSC-90-2218-E-001-005.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Loyola University Chicago, 6525 N. Sheridan Rd., 60626, Chicago, IL

    Michael H. Goldwasser

  2. Department of Computer Science, Northwestern University, 60201, Evanston, IL

    Ming-Yang Kao

  3. Institute of Information Science, Academia Sinica, 128 Academia Road, Section 2, 115, Taipei, Taiwan

    Hsueh-I Lu

Authors
  1. Michael H. Goldwasser
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  2. Ming-Yang Kao
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  3. Hsueh-I Lu
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Editor information

Editors and Affiliations

  1. IMIM-UPF-CRG, Dr. Aiguader 80, 08003, Barcelona, Spain

    Roderic Guigó

  2. Department of Computer Science, University of California, 95616, Davis, CA, USA

    Dan Gusfield

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© 2002 Springer-Verlag Berlin Heidelberg

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Goldwasser, M.H., Kao, MY., Lu, HI. (2002). Fast Algorithms for Finding Maximum-Density Segments of a Sequence with Applications to Bioinformatics. In: Guigó, R., Gusfield, D. (eds) Algorithms in Bioinformatics. WABI 2002. Lecture Notes in Computer Science, vol 2452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45784-4_12

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  • DOI: https://doi.org/10.1007/3-540-45784-4_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44211-0

  • Online ISBN: 978-3-540-45784-8

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