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Dynamic Programming and Fast Matrix Multiplication

  • Conference paper
Algorithms – ESA 2006 (ESA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4168))

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Abstract

We give a novel general approach for solving NP-hard optimization problems that combines dynamic programming and fast matrix multiplication. The technique is based on reducing much of the computation involved to matrix multiplication. We show that our approach works faster than the usual dynamic programming solution for any vertex subset problem on graphs of bounded branchwidth. In particular, we obtain the fastest algorithms for Planar Independent Set of runtime \(O(2^{2.52 \sqrt{n}})\), for Planar Dominating Set of runtime exact \(O(2^{3.99 \sqrt{n}})\) and parameterized \(O(2^{11.98 \sqrt{k}}) \cdot n^{O(1)}\), and for Planar Hamiltonian Cycle of runtime \(O(2^{5.58 \sqrt{n}})\). The exponent of the running time is depending heavily on the running time of the fastest matrix multiplication algorithm that is currently o(n 2.376).

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Author information

Authors and Affiliations

  1. Department of Informatics, University of Bergen, PO Box 7800, 5020, Bergen, Norway

    Frederic Dorn

Authors
  1. Frederic Dorn
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Editors and Affiliations

  1. Microsoft Research, One Microsoft Way, Redmond, WA 98052, USA and School of Computer Science, Tel-Aviv University, 69978, Tel-Aviv, Israel

    Yossi Azar

  2. Department of Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Thomas Erlebach

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© 2006 Springer-Verlag Berlin Heidelberg

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Dorn, F. (2006). Dynamic Programming and Fast Matrix Multiplication. In: Azar, Y., Erlebach, T. (eds) Algorithms – ESA 2006. ESA 2006. Lecture Notes in Computer Science, vol 4168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11841036_27

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  • DOI: https://doi.org/10.1007/11841036_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-38875-3

  • Online ISBN: 978-3-540-38876-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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