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Parameterized Algorithms and Kernels for 3-Hitting Set with Parity Constraints

Kamat, Vikram and Misra, Neeldhara (2015) Parameterized Algorithms and Kernels for 3-Hitting Set with Parity Constraints. In: 9th International Conference on Algorithms and Complexity (CIAC), MAY 20-22, 2015, Univ Paris Dauphine, Paris, FRANCE, pp. 249-260.

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Official URL: http://dx.doi.org/10.1007/978-3-319-18173-8_18

Abstract

The 3-Hitting Set problem involves a family of subsets F of size at most three over an universe U. The goal is to find a subset of U of the smallest possible size that intersects every set in F. The version of the problem with parity constraints asks for a subset S of size at most k that, in addition to being a hitting set, also satisfies certain parity constraints on the sizes of the intersections of S with each set in the family F. In particular, an odd (even) set is a hitting set that hits every set at either one or three (two) elements, and a perfect code is a hitting set that intersects every set at exactly one element. These questions are of fundamental interest in many contexts for general set systems. Just as for Hitting Set, we find these questions to be interesting for the case of families consisting of sets of size at most three. In this work, we initiate an algorithmic study of these problems in this special case, focusing on a parameterized analysis. We show, for each problem, efficient fixed-parameter tractable algorithms using search trees that are tailor-made to the constraints in question, and also polynomial kernels using sunflower-like arguments in a manner that accounts for equivalence under the additional parity constraints.

Item Type: Conference Proceedings
Additional Information: Copy right for this article belongs to the SPRINGER-VERLAG BERLIN, HEIDELBERGER PLATZ 3, D-14197 BERLIN, GERMANY
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Depositing User: Id for Latest eprints
Date Deposited: 30 Oct 2015 06:43
Last Modified: 30 Oct 2015 06:43
URI: http://eprints.iisc.ac.in/id/eprint/52655

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