Space Saving by Dynamic Algebraization Based on Tree-Depth
| Autor: | Martin Fürer, Huiwen Yu |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Tree rotation
Discrete mathematics 0102 computer and information sciences 02 engineering and technology Tree-depth 01 natural sciences Tree decomposition Theoretical Computer Science Combinatorics Treewidth Dynamic programming Tree (data structure) Computational Theory and Mathematics 010201 computation theory & mathematics Theory of computation 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Gomory–Hu tree Mathematics |
| Zdroj: | Theory of Computing Systems. 61:283-304 |
| ISSN: | 1433-0490 1432-4350 |
| DOI: | 10.1007/s00224-017-9751-3 |
| Popis: | 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 ∗(2 h ), where h is the tree-depth (Nesetřil 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. |
| Databáze: | OpenAIRE |
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