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 -