TY - JOUR

T1 - Space Saving by Dynamic Algebraization Based on Tree-Depth

AU - Fürer, Martin

AU - Yu, Huiwen

N1 - Funding Information:
Research supported in part by NSF Grant CCF-0964655 and CCF-1320814
Publisher Copyright:
© 2017, Springer Science+Business Media New York.

PY - 2017/8/1

Y1 - 2017/8/1

N2 - 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.

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 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.

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U2 - 10.1007/s00224-017-9751-3

DO - 10.1007/s00224-017-9751-3

M3 - Article

AN - SCOPUS:85014725050

VL - 61

SP - 283

EP - 304

JO - Theory of Computing Systems

JF - Theory of Computing Systems

SN - 1432-4350

IS - 2

ER -