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Mathematics > Combinatorics

arXiv:1304.4986 (math)
[Submitted on 17 Apr 2013 (v1), last revised 21 Jul 2016 (this version, v3)]

Title:Complexity and polymorphisms for digraph constraint problems under some basic constructions

Authors:Marcel Jackson, Tomasz Kowalski, Todd Niven
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Abstract: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.
Comments: 31 pages
Subjects: Combinatorics (math.CO); Computational Complexity (cs.CC); Discrete Mathematics (cs.DM)
MSC classes: 05C20, 05C15, 08B05
ACM classes: F.2.0; G.2.2
Cite as: arXiv:1304.4986 [math.CO]
  (or arXiv:1304.4986v3 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.1304.4986

Submission history

From: Marcel Jackson G [view email]
[v1] Wed, 17 Apr 2013 23:07:08 UTC (32 KB)
[v2] Sat, 22 Nov 2014 21:01:09 UTC (35 KB)
[v3] Thu, 21 Jul 2016 11:18:29 UTC (38 KB)
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