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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| Vydáno v: | Algorithmica Ročník 52; číslo 2; s. 167 - 176 |
|---|---|
| Hlavní autoři: | , , , , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
Springer-Verlag
01.10.2008
|
| Témata: | |
| 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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| Keywords | Fixed parameter tractable Parameterized complexity Set packing Graph matching Color coding |
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| References | Jia, Zhang, Chen (CR10) 2004; 50 Karp, Miller, Thatcher (CR11) 1972 CR4 CR5 CR8 Woeginger (CR17) 2003 CR7 CR9 CR15 Ausiello, D’Atri, Protasi (CR2) 1980; 21 Koutis (CR13) 2005; 94 CR12 Liu, Lu, Chen, Sze (CR14) 2006 Alon, Yuster, Zwick (CR1) 1995; 42 Fellows (CR6) 2003 Slot, van Emde Boas (CR16) 1985; 21 Chen, Friesen, Jia, Kanj (CR3) 2001 9146_CR15 J. Chen (9146_CR3) 2001 W. Jia (9146_CR10) 2004; 50 G.J. Woeginger (9146_CR17) 2003 Y. Liu (9146_CR14) 2006 M.R. Fellows (9146_CR6) 2003 R.M. Karp (9146_CR11) 1972 9146_CR12 9146_CR9 C.F. Slot (9146_CR16) 1985; 21 9146_CR8 9146_CR5 9146_CR4 9146_CR7 I. Koutis (9146_CR13) 2005; 94 N. Alon (9146_CR1) 1995; 42 G. Ausiello (9146_CR2) 1980; 21 |
| References_xml | – start-page: 84 year: 2006 end-page: 95 ident: CR14 article-title: Greedy localization and color-coding: improved matching and packing algorithms publication-title: Proceedings of the 2nd International Workshop on Parameterized and Exact Computation doi: 10.1007/11847250_8 – volume: 21 start-page: 246 issue: 4/5 year: 1985 end-page: 253 ident: CR16 article-title: On tape versus core; an application of space efficient perfect hash functions to the invariance of space publication-title: Elektron. Inf. Kybern. – ident: CR4 – ident: CR15 – ident: CR12 – volume: 94 start-page: 7 year: 2005 end-page: 9 ident: CR13 article-title: A faster parameterized algorithm for set packing publication-title: Inf. Process. Lett. doi: 10.1016/j.ipl.2004.12.005 – ident: CR9 – start-page: 120 year: 2001 end-page: 131 ident: CR3 article-title: Using nondeterminism to design deterministic algorithms publication-title: Proceedings of the 21st Conference on Foundations of Software Technology and Theoretical Computer Science (FST TCS) doi: 10.1007/3-540-45294-X_11 – start-page: 1 year: 2003 end-page: 12 ident: CR6 article-title: Blow-ups, win/win’s, and crown rules: some new directions in FPT publication-title: Proceedings of the 29th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 03) – start-page: 185 year: 2003 end-page: 207 ident: CR17 article-title: Exact algorithms for NP-hard problems, a survey publication-title: Combinatorial Optimization—Eureka, You Shrink! doi: 10.1007/3-540-36478-1_17 – volume: 21 start-page: 136 year: 1980 end-page: 153 ident: CR2 article-title: Structure preserving reductions among context optimization problems publication-title: J. Comput. Syst. Sci. doi: 10.1016/0022-0000(80)90046-X – ident: CR5 – ident: CR7 – ident: CR8 – start-page: 85 year: 1972 end-page: 103 ident: CR11 article-title: Reducibility among combinatorial problems publication-title: Complexity of Computer Computations – volume: 50 start-page: 106 issue: 1 year: 2004 end-page: 117 ident: CR10 article-title: An efficient parameterized algorithm for -set packing publication-title: J. Algorithms doi: 10.1016/j.jalgor.2003.07.001 – volume: 42 start-page: 844 issue: 4 year: 1995 end-page: 856 ident: CR1 article-title: Color-coding publication-title: J. Assoc. Comput. Mach. – volume: 94 start-page: 7 year: 2005 ident: 9146_CR13 publication-title: Inf. Process. Lett. doi: 10.1016/j.ipl.2004.12.005 – ident: 9146_CR4 – volume: 21 start-page: 136 year: 1980 ident: 9146_CR2 publication-title: J. Comput. Syst. Sci. doi: 10.1016/0022-0000(80)90046-X – ident: 9146_CR7 doi: 10.1007/978-3-540-30559-0_20 – volume: 50 start-page: 106 issue: 1 year: 2004 ident: 9146_CR10 publication-title: J. Algorithms doi: 10.1016/j.jalgor.2003.07.001 – ident: 9146_CR5 doi: 10.1007/978-3-540-30559-0_22 – start-page: 1 volume-title: Proceedings of the 29th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 03) year: 2003 ident: 9146_CR6 doi: 10.1007/978-3-540-39890-5_1 – start-page: 85 volume-title: Complexity of Computer Computations year: 1972 ident: 9146_CR11 doi: 10.1007/978-1-4684-2001-2_9 – volume: 42 start-page: 844 issue: 4 year: 1995 ident: 9146_CR1 publication-title: J. Assoc. Comput. Mach. doi: 10.1145/210332.210337 – ident: 9146_CR12 doi: 10.1007/11917496_6 – ident: 9146_CR9 doi: 10.1109/SFCS.1982.39 – start-page: 120 volume-title: Proceedings of the 21st Conference on Foundations of Software Technology and Theoretical Computer Science (FST TCS) year: 2001 ident: 9146_CR3 doi: 10.1007/3-540-45294-X_11 – start-page: 185 volume-title: Combinatorial Optimization—Eureka, You Shrink! year: 2003 ident: 9146_CR17 doi: 10.1007/3-540-36478-1_17 – volume: 21 start-page: 246 issue: 4/5 year: 1985 ident: 9146_CR16 publication-title: Elektron. Inf. Kybern. – ident: 9146_CR8 doi: 10.1007/978-3-540-30140-0_29 – ident: 9146_CR15 doi: 10.1109/CCC.2004.1313823 – start-page: 84 volume-title: Proceedings of the 2nd International Workshop on Parameterized and Exact Computation year: 2006 ident: 9146_CR14 doi: 10.1007/11847250_8 |
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| Snippet | 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... |
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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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