### 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.

Original language | English (US) |
---|---|

Title of host publication | Computer Science Theory and Applications - 9th International Computer Science Symposium in Russia, CSR 2014, Proceedings |

Publisher | Springer Verlag |

Pages | 375-388 |

Number of pages | 14 |

ISBN (Print) | 9783319066851 |

DOIs | |

State | Published - Jan 1 2014 |

Event | 9th International Computer Science Symposium in Russia, CSR 2014 - Moscow, Russian Federation Duration: Jun 7 2014 → Jun 11 2014 |

### Publication series

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

Volume | 8476 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

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

Country | Russian Federation |

City | Moscow |

Period | 6/7/14 → 6/11/14 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Computer Science Theory and Applications - 9th International Computer Science Symposium in Russia, CSR 2014, Proceedings*(pp. 375-388). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8476 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-06686-8_29

}

*Computer Science Theory and Applications - 9th International Computer Science Symposium in Russia, CSR 2014, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8476 LNCS, Springer Verlag, pp. 375-388, 9th International Computer Science Symposium in Russia, CSR 2014, Moscow, Russian Federation, 6/7/14. https://doi.org/10.1007/978-3-319-06686-8_29

**Space saving by dynamic algebraization.** / Furer, Martin; Yu, Huiwen.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Space saving by dynamic algebraization

AU - Furer, Martin

AU - Yu, Huiwen

PY - 2014/1/1

Y1 - 2014/1/1

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 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

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

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

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

M3 - Conference contribution

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

ER -