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Space Saving by Dynamic Algebraization

  • Martin Fürer
  • Huiwen Yu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8476)

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.

Keywords

Dynamic programming tree decomposition space-efficient algorithm exponential time algorithms zeta transform 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Martin Fürer
    • 1
  • Huiwen Yu
    • 1
  1. 1.Department of Computer Science and EngineeringThe Pennsylvania State UniversityUniversity ParkUSA

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