A kernelization algorithm for d-Hitting Set

For a given parameterized problem, π, a kernelization algorithm is a polynomial-time pre-processing procedure that transforms an arbitrary instance of π into an equivalent one whose size depends only on the input parameter(s). The resulting instance is called a problem kernel. In this paper, a kerne...

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Bibliographic Details
Published in:Journal of computer and system sciences Vol. 76; no. 7; pp. 524 - 531
Main Author: Abu-Khzam, Faisal N.
Format: Journal Article
Language:English
Published: Elsevier Inc 01.11.2010
Subjects:
Algorithms
Crown decomposition
Equivalence
Fixed-parameter algorithms
Hitting Set
Hypergraphs
Kernelization
Kernels
Transforms
Vertex cover
Crown decomposition
Vertex cover
Hitting Set
Fixed-parameter algorithms
Hypergraphs
Kernelization
ISSN:0022-0000, 1090-2724
Online Access:Get full text
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Summary:For a given parameterized problem, π, a kernelization algorithm is a polynomial-time pre-processing procedure that transforms an arbitrary instance of π into an equivalent one whose size depends only on the input parameter(s). The resulting instance is called a problem kernel. In this paper, a kernelization algorithm for the 3-Hitting Set problem is presented along with a general kernelization for d-Hitting Set. For 3-Hitting Set, an arbitrary instance is reduced into an equivalent one that contains at most 5 k 2 + k elements. This kernelization is an improvement over previously known methods that guarantee cubic-order kernels. Our method is used also to obtain quadratic kernels for several other problems. For a constant d ⩾ 3 , a kernelization of d-Hitting Set is achieved by a non-trivial generalization of the 3-Hitting Set method, and guarantees a kernel whose order does not exceed ( 2 d − 1 ) k d − 1 + k .
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ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2009.09.002