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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| Veröffentlicht in: | Algorithmica Jg. 52; H. 2; S. 167 - 176 |
|---|---|
| Hauptverfasser: | , , , , , , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
New York
Springer-Verlag
01.10.2008
|
| Schlagworte: | |
| ISSN: | 0178-4617, 1432-0541 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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. |
|---|---|
| ISSN: | 0178-4617 1432-0541 |
| DOI: | 10.1007/s00453-007-9146-y |