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- W2783180493 abstract "This paper is concerned with the design and analysis of approximation algorithms for the problem of finding the least weight refutation in a weighted difference constraint system (DCS). In a weighted DCS (WDCS), a positive weight is associated with each constraint. Every infeasible DCS has a refutation, which attests to its infeasibility. The length of a refutation is the number of constraints used in the derivation of a contradiction. Associated with a DCS (mathbf{D}) is its constraint network (mathbf{G}). (mathbf{D}) is infeasible if and only if (mathbf{G}) has a simple, negative cost cycle. It follows that the shortest refutation of (mathbf{D}) corresponds to the length of the shortest negative cost cycle in (mathbf{G}). The constraint network of a WDCS is represented by a constraint network, where each edge contains both a cost and a positive, integral length. In the case of a WDCS, the weight of a refutation is defined as the sum of the lengths of the edges corresponding to the refutation. The problem of finding the minimum weight refutation in a WDCS is called the weighted optimal length resolution refutation (WOLRR) problem and is known to be NP-hard. In this paper, we describe a pseudo-polynomial time algorithm for the WOLRR problem and convert it into a fully polynomial time approximation scheme (FPTAS). We also generalize our FPTAS to determine the optimal length refutation of a class of constraints called Unit Two Variable per Inequality (UTVPI) constraints." @default.
- W2783180493 created "2018-01-26" @default.
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- W2783180493 date "2018-01-01" @default.
- W2783180493 modified "2023-10-08" @default.
- W2783180493 title "A Fully Polynomial Time Approximation Scheme for Refutations in Weighted Difference Constraint Systems" @default.
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- W2783180493 doi "https://doi.org/10.1007/978-3-319-74180-2_4" @default.
- W2783180493 hasPublicationYear "2018" @default.
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