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Erschienen in:
2009 | OriginalPaper | Buchkapitel
Improved Deterministic Algorithms for Weighted Matching and Packing Problems
verfasst von : Qilong Feng, Yang Liu, Songjian Lu, Jianxin Wang
Erschienen in: Theory and Applications of Models of Computation
Verlag: Springer Berlin Heidelberg
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For the weighted
r
D-Matching problem, we present a deterministic parameterized algorithm with time complexity
O
*
(4
(
r
− 1)
k
), improving the previous best upper bound
O
*
(4
rk
). In particular, the algorithm can be applied to solve the unweighted 3D-Matching problem with time
O
*
(16
k
), improving the previous best result
O
*
(21.26
k
). For the weighted
r
-Set Packing problem, we present a deterministic parameterized algorithm with time complexity
O
*
(2
(2
r
− 1)
k
), improving the previous best result
O
*
(2
2
rk
). The algorithm, when applied to the unweighted 3-Set Packing problem, has running time
O
*
(32
k
), improving the previous best result
O
*
(43.62
k
). Moreover, for the weighted
r
D-Matching and weighted
r
-Set Packing problems, we get a kernel of size
O
(
k
r
).