Faster Fixed-Parameter Tractable Algorithms for Matching and Packing Problems

We obtain faster algorithms for problems such as r -dimensional matching and r -set packing when the size k of the solution is considered a parameter. We first establish a general framework for finding and exploiting small problem kernels (of size polynomial in k ). This technique lets us combine Al...

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Published in:	Algorithmica Vol. 52; no. 2; pp. 167 - 176
Main Authors:	Fellows, M. R., Knauer, C., Nishimura, N., Ragde, P., Rosamond, F., Stege, U., Thilikos, D. M., Whitesides, S.
Format:	Journal Article
Language:	English
Published:	New York Springer-Verlag 01.10.2008
Subjects:	Algorithm Analysis and Problem Complexity Algorithms Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Mathematics of Computing Theory of Computation Fixed parameter tractable Parameterized complexity Set packing Graph matching Color coding
ISSN:	0178-4617, 1432-0541
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Abstract	We obtain faster algorithms for problems such as r -dimensional matching and r -set packing when the size k of the solution is considered a parameter. We first establish a general framework for finding and exploiting small problem kernels (of size polynomial in k ). This technique lets us combine Alon, Yuster and Zwick’s color-coding technique with dynamic programming to obtain faster fixed-parameter algorithms for these problems. Our algorithms run in time O ( n +2 O ( k ) ), an improvement over previous algorithms for some of these problems running in time O ( n + k O ( k ) ). The flexibility of our approach allows tuning of algorithms to obtain smaller constants in the exponent.
AbstractList	We obtain faster algorithms for problems such as r -dimensional matching and r -set packing when the size k of the solution is considered a parameter. We first establish a general framework for finding and exploiting small problem kernels (of size polynomial in k ). This technique lets us combine Alon, Yuster and Zwick’s color-coding technique with dynamic programming to obtain faster fixed-parameter algorithms for these problems. Our algorithms run in time O ( n +2 O ( k ) ), an improvement over previous algorithms for some of these problems running in time O ( n + k O ( k ) ). The flexibility of our approach allows tuning of algorithms to obtain smaller constants in the exponent.
Author	Rosamond, F. Knauer, C. Fellows, M. R. Thilikos, D. M. Stege, U. Ragde, P. Nishimura, N. Whitesides, S.
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Cites_doi	10.1007/11847250_8 10.1016/j.ipl.2004.12.005 10.1007/3-540-45294-X_11 10.1007/3-540-36478-1_17 10.1016/0022-0000(80)90046-X 10.1016/j.jalgor.2003.07.001 10.1007/978-3-540-30559-0_20 10.1007/978-3-540-30559-0_22 10.1007/978-3-540-39890-5_1 10.1007/978-1-4684-2001-2_9 10.1145/210332.210337 10.1007/11917496_6 10.1109/SFCS.1982.39 10.1007/978-3-540-30140-0_29 10.1109/CCC.2004.1313823
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SubjectTerms	Algorithm Analysis and Problem Complexity Algorithms Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Mathematics of Computing Theory of Computation
Title	Faster Fixed-Parameter Tractable Algorithms for Matching and Packing Problems
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