2026-07-20T11:15:06Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:4702 2024-03-06T10:35:16Z ddc:004 open_access

Universal Factor Graphs for Every NP-Hard Boolean CSP Jozeph, Shlomo Hardness of Approximation Hardness with Preprocessing 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. This 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Shlomo Jozeph 2014 Is Part Of LIPIcs, Volume 28, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX-RANDOM.2014.274 urn:nbn:de:0030-drops-47021 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.274 eng https://creativecommons.org/licenses/by/3.0/legalcode