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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Packing-Based Approximation Algorithm for the k-Set Cover Problem
verfasst von : Martin Fürer, Huiwen Yu
Erschienen in: Algorithms and Computation
Verlag: Springer Berlin Heidelberg
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We present a packing-based approximation algorithm for the
k
-Set Cover problem. We introduce a new local search-based
k
-set packing heuristic, and call it Restricted
k
-Set Packing. We analyze its tight approximation ratio via a complicated combinatorial argument. Equipped with the Restricted
k
-Set Packing algorithm, our
k
-Set Cover algorithm is composed of the
k
-Set Packing heuristic [8] for
k
≥ 7, Restricted
k
-Set Packing for
k
= 6,5,4 and the semi-local (2,1)-improvement [2] for 3-Set Cover. We show that our algorithm obtains a tight approximation ratio of
$H_k-0.6402+\Theta(\frac{1}{k})$
, where
H
k
is the
k
-th harmonic number. For small
k
, our results are 1.8667 for
k
= 6, 1.7333 for
k
= 5 and 1.5208 for
k
= 4. Our algorithm improves the currently best approximation ratio for the
k
-Set Cover problem of any
k
≥ 4.