Space saving by dynamic algebraization

Martin Furer, Huiwen Yu

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    2 Citations (Scopus)

    Abstract

    Dynamic programming is widely used for exact computations based on tree decompositions of graphs. However, the space complexity is usually exponential in the treewidth. We study the problem of designing efficient dynamic programming algorithm based on tree decompositions in polynomial space. We show how to construct a tree decomposition and extend the algebraic techniques of Lokshtanov and Nederlof [18] such that the dynamic programming algorithm runs in time O *(2 h ), where h is the maximum number of vertices in the union of bags on the root to leaf paths on a given tree decomposition, which is a parameter closely related to the tree-depth of a graph [21]. We apply our algorithm to the problem of counting perfect matchings on grids and show that it outperforms other polynomial-space solutions. We also apply the algorithm to other set covering and partitioning problems.

    Original languageEnglish (US)
    Title of host publicationComputer Science Theory and Applications - 9th International Computer Science Symposium in Russia, CSR 2014, Proceedings
    PublisherSpringer Verlag
    Pages375-388
    Number of pages14
    ISBN (Print)9783319066851
    DOIs
    StatePublished - Jan 1 2014
    Event9th International Computer Science Symposium in Russia, CSR 2014 - Moscow, Russian Federation
    Duration: Jun 7 2014Jun 11 2014

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume8476 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other9th International Computer Science Symposium in Russia, CSR 2014
    CountryRussian Federation
    CityMoscow
    Period6/7/146/11/14

    Fingerprint

    Tree Decomposition
    Dynamic programming
    Decomposition
    Dynamic Programming
    Polynomials
    Set Partitioning
    Set Covering
    Exact Computation
    Polynomial
    Treewidth
    Trees (mathematics)
    Space Complexity
    Perfect Matching
    Graph in graph theory
    Counting
    Leaves
    Union
    Roots
    Grid
    Path

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Furer, M., & Yu, H. (2014). Space saving by dynamic algebraization. In Computer Science Theory and Applications - 9th International Computer Science Symposium in Russia, CSR 2014, Proceedings (pp. 375-388). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8476 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-06686-8_29
    Furer, Martin ; Yu, Huiwen. / Space saving by dynamic algebraization. Computer Science Theory and Applications - 9th International Computer Science Symposium in Russia, CSR 2014, Proceedings. Springer Verlag, 2014. pp. 375-388 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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    Furer, M & Yu, H 2014, Space saving by dynamic algebraization. in Computer Science Theory and Applications - 9th International Computer Science Symposium in Russia, CSR 2014, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8476 LNCS, Springer Verlag, pp. 375-388, 9th International Computer Science Symposium in Russia, CSR 2014, Moscow, Russian Federation, 6/7/14. https://doi.org/10.1007/978-3-319-06686-8_29

    Space saving by dynamic algebraization. / Furer, Martin; Yu, Huiwen.

    Computer Science Theory and Applications - 9th International Computer Science Symposium in Russia, CSR 2014, Proceedings. Springer Verlag, 2014. p. 375-388 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8476 LNCS).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

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    AB - Dynamic programming is widely used for exact computations based on tree decompositions of graphs. However, the space complexity is usually exponential in the treewidth. We study the problem of designing efficient dynamic programming algorithm based on tree decompositions in polynomial space. We show how to construct a tree decomposition and extend the algebraic techniques of Lokshtanov and Nederlof [18] such that the dynamic programming algorithm runs in time O *(2 h ), where h is the maximum number of vertices in the union of bags on the root to leaf paths on a given tree decomposition, which is a parameter closely related to the tree-depth of a graph [21]. We apply our algorithm to the problem of counting perfect matchings on grids and show that it outperforms other polynomial-space solutions. We also apply the algorithm to other set covering and partitioning problems.

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    Furer M, Yu H. Space saving by dynamic algebraization. In Computer Science Theory and Applications - 9th International Computer Science Symposium in Russia, CSR 2014, Proceedings. Springer Verlag. 2014. p. 375-388. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-06686-8_29