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Solving MIN ONES 2-SAT as fast as VERTEX COVER

Misra, Neeldhara and Narayanaswamy, NS and Raman, Venkatesh and Shankar, Bal Sri (2013) Solving MIN ONES 2-SAT as fast as VERTEX COVER. In: THEORETICAL COMPUTER SCIENCE, 506 . pp. 115-121.

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Official URL: http://dx.doi.org/10.1016/j.tcs.2013.07.019

Abstract

The problem of finding a satisfying assignment that minimizes the number of variables that are set to 1 is NP-complete even for a satisfiable 2-SAT formula. We call this problem MIN ONES 2-SAT. It generalizes the well-studied problem of finding the smallest vertex cover of a graph, which can be modeled using a 2-SAT formula with no negative literals. The natural parameterized version of the problem asks for a satisfying assignment of weight at most k. In this paper, we present a polynomial-time reduction from MIN ONES 2-SAT to VERTEX COVER without increasing the parameter and ensuring that the number of vertices in the reduced instance is equal to the number of variables of the input formula. Consequently, we conclude that this problem also has a simple 2-approximation algorithm and a 2k - c logk-variable kernel subsuming (or, in the case of kernels, improving) the results known earlier. Further, the problem admits algorithms for the parameterized and optimization versions whose runtimes will always match the runtimes of the best-known algorithms for the corresponding versions of vertex cover. Finally we show that the optimum value of the LP relaxation of the MIN ONES 2-SAT and that of the corresponding VERTEX COVER are the same. This implies that the (recent) results of VERTEX COVER version parameterized above the optimum value of the LP relaxation of VERTEX COVER carry over to the MIN ONES 2-SAT version parameterized above the optimum of the LP relaxation of MIN ONES 2-SAT. (C) 2013 Elsevier B.V. All rights reserved.

Item Type: Journal Article
Additional Information: copyright for this article belongs to ELSEVIER SCIENCE
Keywords: MIN ONES 2-SAT; VERTEX COVER; Linear programming relaxation; Parameterized complexity
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Depositing User: Id for Latest eprints
Date Deposited: 26 Nov 2013 15:19
Last Modified: 26 Nov 2013 15:19
URI: http://eprints.iisc.ac.in/id/eprint/47793

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