{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article7600","name":"Universal Factor Graphs for Every NP-Hard Boolean CSP","abstract":"An instance of a Boolean constraint satisfaction problem can be divided into two parts. One part, that we refer to as the factor graph of the instance, specifies for each clause the set of variables that are associated with the clause. The other part, specifies for each of the given clauses what is the constraint that is evaluated on the respective variables. Depending on the allowed choices of constraints, it is known that Boolean constraint satisfaction problems fall into one of two classes, being either NP-hard or in P.\r\n\r\nThis paper shows that every NP-hard Boolean constraint satisfaction problem (except for an easy to characterize set of natural exceptions) has a universal factor graph. That is, for every NP-hard Boolean constraint satisfaction problem, there is a family of at most one factor graph of each size, such that the problem, restricted to instances that have a factor graph from this family, cannot be solved in polynomial time unless NP is contained in P\/poly. Moreover, we extend this classification to one that establishes hardness of approximation.","keywords":["Hardness of Approximation","Hardness with Preprocessing"],"author":{"@type":"Person","name":"Jozeph, Shlomo","givenName":"Shlomo","familyName":"Jozeph"},"position":19,"pageStart":274,"pageEnd":283,"dateCreated":"2014-09-04","datePublished":"2014-09-04","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Jozeph, Shlomo","givenName":"Shlomo","familyName":"Jozeph"},"copyrightYear":"2014","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.APPROX-RANDOM.2014.274","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6231","volumeNumber":28,"name":"Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX\/RANDOM 2014)","dateCreated":"2014-09-04","datePublished":"2014-09-04","editor":[{"@type":"Person","name":"Jansen, Klaus","givenName":"Klaus","familyName":"Jansen"},{"@type":"Person","name":"Rolim, Jos\u00e9","givenName":"Jos\u00e9","familyName":"Rolim"},{"@type":"Person","name":"Devanur, Nikhil R.","givenName":"Nikhil R.","familyName":"Devanur"},{"@type":"Person","name":"Moore, Cristopher","givenName":"Cristopher","familyName":"Moore"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article7600","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6231"}}}