2013/04/17 by Marcel Jackson, Tomasz Kowalski, Jackson, Marcel +3
Computer Science · Mathematics · #05C15 #05C20 #08B05 #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Complexity (cs.CC) #Constraint Satisfaction and Optimization #Discrete Mathematics (cs.DM) #F.2.0 #FOS: Computer and information sciences #FOS: Mathematics #G.2.2 #acm:05C15 #acm:05C20 #acm:08B05 #cs.CC #cs.DM #math.CO #msc:05C15 #msc:05C20 #msc:08B05
paper · pdf · doi:10.48550/arxiv.1304.4986
31 pages
openalex publication_date 2013/04/17 · arxiv created 2016/07/21 · arxiv updated 2016/07/22 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
The role of polymorphisms in determining the complexity of constraint satisfaction problems is well established. In this context we study the stability of CSP complexity and polymorphism properties under some basic graph theoretic constructions. As applications we observe a collapse in the applicability of algorithms for CSPs over directed graphs with both a total source and a total sink: the corresponding CSP is solvable by the "few subpowers algorithm" if and only if it is solvable by a local consistency check algorithm. Moreover, we find that the property of "strict width" and solvability by few subpowers are unstable under first order reductions. The analysis also yields a complete characterisation of the main polymorphism properties for digraphs whose symmetric closure is a complete graph.