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Subquadratic Algorithm for Dynamic Shortest Distances

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Computing and Combinatorics (COCOON 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3595))

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Abstract

In this paper we extend a technique introduced in [14] for dynamic matrix functions. We present dynamic algorithms for computing matrix determinant and matrix adjoint over commutative rings. These algorithms are then used to construct an algorithm for dynamic shortest distances in unweighted graph. Our algorithm supports updates in O(n 1.932) randomized time and queries in O(n 1.288) randomized time. These bound improve over the previous results and solve a long-standing open problem if sub-quadratic dynamic algorithms exist for computing all pairs shortest distances.

Research supported by KBN grant 4T11C04425

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Authors and Affiliations

  1. Institute of Informatics, Warsaw University, ul. Banacha 2, 02-097, Warsaw, Poland

    Piotr Sankowski

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  1. Piotr Sankowski
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Editors and Affiliations

  1. Department of Computer Science, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong

    Lusheng Wang

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© 2005 Springer-Verlag Berlin Heidelberg

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Sankowski, P. (2005). Subquadratic Algorithm for Dynamic Shortest Distances. In: Wang, L. (eds) Computing and Combinatorics. COCOON 2005. Lecture Notes in Computer Science, vol 3595. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11533719_47

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  • DOI: https://doi.org/10.1007/11533719_47

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28061-3

  • Online ISBN: 978-3-540-31806-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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