Constraint satisfaction problems parameterized above or below tight bounds: A survey

Gregory Gutin*, Anders Yeo

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingBook chapterResearchpeer-review

Abstract

We consider constraint satisfaction problems parameterized above or below tight bounds. One example is MaxSat parameterized above m/2: given a CNF formula F with m clauses, decide whether there is a truth assignment that satisfies at least m/2+k clauses, where k is the parameter. Among other problems we deal with are MaxLin2-AA (given a system of linear equations over F in which each equation has a positive integral weight, decide whether there is an assignment to the variables that satisfies equations of total weight at least W/2+k, where W is the total weight of all equations), Max-r-Lin2-AA (the same as MaxLin2-AA, but each equation has at most r variables, where r is a constant) and Max-r-Sat-AA (given a CNF formula F with m clauses in which each clause has at most r literals, decide whether there is a truth assignment satisfying at least ∑ m i=1 (1-2 r i clauses, where k is the parameter, r i is the number of literals in Clause i, and r is a constant). We also consider Max-r-CSP-AA, a natural generalization of both Max-r-Lin2-AA and Max-r-Sat-AA, order (or, permutation) constraint satisfaction problems of arities 2 and 3 parameterized above the average value and some other problems related to MaxSat. We discuss results, both polynomial kernels and parameterized algorithms, obtained for the problems mainly in the last few years as well as some open questions.

Original languageEnglish
Title of host publicationThe Multivariate Algorithmic Revolution and Beyond : Essays Dedicated to Michael R. Fellows on the Occasion of His 60th Birthday
Volume7370
PublisherSpringer
Publication date2012
Pages257-286
ISBN (Print)9783642308901
ISBN (Electronic)978-3-642-30891-8
DOIs
Publication statusPublished - 2012
Externally publishedYes
SeriesLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7370
ISSN0302-9743

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