TY - GEN

T1 - Space saving by dynamic algebraization

AU - Fürer, Martin

AU - Yu, Huiwen

PY - 2014

Y1 - 2014

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 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84958529448&partnerID=8YFLogxK

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U2 - 10.1007/978-3-319-06686-8_29

DO - 10.1007/978-3-319-06686-8_29

M3 - Conference contribution

AN - SCOPUS:84958529448

SN - 9783319066851

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 375

EP - 388

BT - Computer Science Theory and Applications - 9th International Computer Science Symposium in Russia, CSR 2014, Proceedings

PB - Springer Verlag

T2 - 9th International Computer Science Symposium in Russia, CSR 2014

Y2 - 7 June 2014 through 11 June 2014

ER -