Bannach, Max ;
Skambath, Malte ;
Tantau, Till
Kernelizing the Hitting Set Problem in Linear Sequential and Constant Parallel Time
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 easytocheck size properties. The rule states that the link of a critical c can be replaced by c. It is known that a simple lineartime 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 polynomialsize kernels. Previously, such algorithms were not even known for artificial problems. An interesting application of our methods lies in traditional, nonparameterized approximation theory: Our results imply that uniform AC⁰circuits 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 = {9:19:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959771504},
ISSN = {18688969},
year = {2020},
volume = {162},
editor = {Susanne Albers},
publisher = {Schloss DagstuhlLeibnizZentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/12256},
URN = {urn:nbn:de:0030drops122566},
doi = {10.4230/LIPIcs.SWAT.2020.9},
annote = {Keywords: Kernelization, Approximation, Hitting Set, ConstantDepth Circuits}
}
12.06.2020
Keywords: 

Kernelization, Approximation, Hitting Set, ConstantDepth Circuits 
Seminar: 

17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)

Issue date: 

2020 
Date of publication: 

12.06.2020 