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A Sub-cubic Time Algorithm for the k-Maximum Subarray Problem

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Algorithms and Computation (ISAAC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4835))

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Abstract

We design a faster algorithm for the k-maximum sub-array problem under the conventional RAM model, based on distance matrix multiplication (DMM). Specifically we achieve \(O(n^3\sqrt{\log\log n/\log n} + k\log n)\) for a general problem where overlapping is allowed for solution arrays. This complexity is sub-cubic when k = o(n 3/logn). The best known complexities of this problem are O(n 3 + klogn), which is cubic when k = O(n 3/logn), and \(O(kn^3\sqrt{\log\log n/\log n})\), which is sub-cubic when \(k=o(\sqrt{\log n/\log\log n})\).

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Authors and Affiliations

  1. Department of Computer Science, University of Canterbury, Christchurch, New Zealand

    Sung Eun Bae & Tadao Takaoka

Authors
  1. Sung Eun Bae
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  2. Tadao Takaoka
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Takeshi Tokuyama

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Bae, S.E., Takaoka, T. (2007). A Sub-cubic Time Algorithm for the k-Maximum Subarray Problem. In: Tokuyama, T. (eds) Algorithms and Computation. ISAAC 2007. Lecture Notes in Computer Science, vol 4835. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77120-3_65

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  • DOI: https://doi.org/10.1007/978-3-540-77120-3_65

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77118-0

  • Online ISBN: 978-3-540-77120-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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