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Consequences of Faster Alignment of Sequences

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Book cover Automata, Languages, and Programming (ICALP 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8572))

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Abstract

The Local Alignment problem is a classical problem with applications in biology. Given two input strings and a scoring function on pairs of letters, one is asked to find the substrings of the two input strings that are most similar under the scoring function. The best algorithms for Local Alignment run in time that is roughly quadratic in the string length. It is a big open problem whether substantially subquadratic algorithms exist. In this paper we show that for all ε > 0, an O(n 2 − ε) time algorithm for Local Alignment on strings of length n would imply breakthroughs on three longstanding open problems: it would imply that for some δ > 0, 3SUM on n numbers is in O(n 2 − δ) time, CNF-SAT on n variables is in O((2 − δ)n) time, and Max Weight 4-Clique is in O(n 4 − δ) time. Our result for CNF-SAT also applies to the easier problem of finding the longest common substring of binary strings with don’t cares. We also give strong conditional lower bounds for the more general Multiple Local Alignment problem on k strings, under both k-wise and SP scoring, and for other string similarity problems such as Global Alignment with gap penalties and normalized Longest Common Subsequence.

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Author information

Authors and Affiliations

  1. Stanford University, USA

    Amir Abboud & Virginia Vassilevska Williams

  2. University of Haifa, Israel

    Oren Weimann

Authors
  1. Amir Abboud
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  2. Virginia Vassilevska Williams
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  3. Oren Weimann
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Technische Universität München, Boltzmannstrasse 3, 85748, München, Germany

    Javier Esparza

  2. LIAFA, Université Paris Diderot-Paris 7, Case 7014, 75205, Paris Cedex 13, France

    Pierre Fraigniaud

  3. IT University of Copenhagen, Rued Langgaards Vej 7, 2300, Copenhagen, Denmark

    Thore Husfeldt

  4. Department Computer Science, University of Oxford, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Elias Koutsoupias

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Abboud, A., Williams, V.V., Weimann, O. (2014). Consequences of Faster Alignment of Sequences. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds) Automata, Languages, and Programming. ICALP 2014. Lecture Notes in Computer Science, vol 8572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43948-7_4

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  • DOI: https://doi.org/10.1007/978-3-662-43948-7_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-43947-0

  • Online ISBN: 978-3-662-43948-7

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