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DOI: 10.4230/LIPIcs.SWAT.2020.9
URN: urn:nbn:de:0030-drops-122566
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12256/
Bannach, Max ; Skambath, Malte ; Tantau, Till
Kernelizing the Hitting Set Problem in Linear Sequential and Constant Parallel Time
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Abstract
We analyze a reduction rule for computing kernels for the hitting set problem: In a hypergraph, the link of a set c of vertices consists of all edges that are supersets of c. We call such a set critical if its link has certain easy-to-check size properties. The rule states that the link of a critical c can be replaced by c. It is known that a simple linear-time algorithm for computing hitting set kernels (number of edges) at most k^d (k is the hitting set size, d is the maximum edge size) can be derived from this rule. We parallelize this algorithm and obtain the first AC⁰ kernel algorithm that outputs polynomial-size kernels. Previously, such algorithms were not even known for artificial problems. An interesting application of our methods lies in traditional, non-parameterized approximation theory: Our results imply that uniform AC⁰-circuits can compute a hitting set whose size is polynomial in the size of an optimal hitting set.
BibTeX - Entry
@InProceedings{bannach_et_al:LIPIcs:2020:12256,
author = {Max Bannach and Malte Skambath and Till Tantau},
title = {{Kernelizing the Hitting Set Problem in Linear Sequential and Constant Parallel Time}},
booktitle = {17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)},
pages = {9:1--9:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-150-4},
ISSN = {1868-8969},
year = {2020},
volume = {162},
editor = {Susanne Albers},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/12256},
URN = {urn:nbn:de:0030-drops-122566},
doi = {10.4230/LIPIcs.SWAT.2020.9},
annote = {Keywords: Kernelization, Approximation, Hitting Set, Constant-Depth Circuits}
}
| Keywords: | Kernelization, Approximation, Hitting Set, Constant-Depth Circuits | |
| Seminar: | 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020) | |
| Issue date: | 2020 | |
| Date of publication: | 12.06.2020 |
