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Efficient algorithms for solving systems of linear equations and path problems

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STACS 92 (STACS 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 577))

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Abstract

Efficient algorithms are presented for solving systems of linear equations defined on and for solving path problems [11] for treewidth k graphs [20] and for α-near-planar graphs [22]. These algorithms include the following:

  1. 1.

    O(nk2) and O(n3/2) time algorithms for solving a system of linear equations and for solving the single source shortest path problem,

  2. 2.

    O(n2k) and O(n2log n) time algorithms for computing A−1 where A is an n×n matrix over a field or for computing A* where A is an n×n matrix over a closed semiring, and

  3. 3.

    O(n2k) and O(n2log n) time algorithms for the all pairs shortest path problems.

One corollary of these results is that the single source and all pairs shortest path problems are solvable in O(n) and O(n2) steps, respectively, for any of the decomposable graph classes in [5].

Supported in part by NSF Grant CCR 89-03319. Address: Department of Computer Science, SUNY at Albany, Albany, NY 12222,USA.

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Authors and Affiliations

  1. University at Albany, Suny, USA

    Venkatesh Radhakrishnan, Harry B. Hunt III & Richard E. Stearns

Authors
  1. Venkatesh Radhakrishnan
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  2. Harry B. Hunt III
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  3. Richard E. Stearns
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Alain Finkel Matthias Jantzen

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© 1992 Springer-Verlag Berlin Heidelberg

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Radhakrishnan, V., Hunt, H.B., Stearns, R.E. (1992). Efficient algorithms for solving systems of linear equations and path problems. In: Finkel, A., Jantzen, M. (eds) STACS 92. STACS 1992. Lecture Notes in Computer Science, vol 577. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55210-3_177

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  • DOI: https://doi.org/10.1007/3-540-55210-3_177

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  • Print ISBN: 978-3-540-55210-9

  • Online ISBN: 978-3-540-46775-5

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