Combinatorial Proof that Subprojective Constraint Satisfaction Problems are NP-Complete

Abstract. We introduce a new general polynomial-time constructionthe fibre construction- which reduces any constraint satisfaction problem CSP(H) to the constraint satisfaction problem CSP(P), where P is any subprojective relational structure. As a consequence we get a new proof (not using universal algebra) that CSP(P) is NP-complete for any subprojective (and thus also projective) relational structure. This provides a starting point for a new combinatorial approach to the NP-completeness part of the conjectured Dichotomy Classification of CSPs, which was previously obtained by algebraic methods. This approach is flexible enough to yield NP-completeness of coloring problems with large girth and bounded degree restrictions.

• Type: Conference
• Year: 2007
• Where: MFCS
• Authors: Jaroslav Nesetril, Mark H. Siggers
• Keywords: Constraint Satisfaction Problem, MFCS 2007, Relational Structure, Subprojective Relational Structure