Space Saving by Dynamic Algebraization Based on Tree-Depth

Martin Fürer, Huiwen Yu

    Research output: Contribution to journalArticlepeer-review

    8 Scopus citations


    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 algorithms based on tree decompositions in polynomial space. We show how to use a tree decomposition and extend the algebraic techniques of Lokshtanov and Nederlof (In: 42nd ACM Symposium on Theory of Computing, pp. 321–330, 2010) such that a typical dynamic programming algorithm runs in time O(2h), where h is the tree-depth (Nešetřil et al., Eur. J. Comb. 27(6):1022–1041, 2006) of a graph. In general, we assume that a tree decomposition of depth h is given. 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)
    Pages (from-to)283-304
    Number of pages22
    JournalTheory of Computing Systems
    Issue number2
    StatePublished - Aug 1 2017

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computational Theory and Mathematics


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