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Jakub Bulín ; Dejan Delic ; Marcel Jackson ; Todd Niven - A finer reduction of constraint problems to digraphs
lmcs:1619 - Logical Methods in Computer Science, December 29, 2015, Volume 11, Issue 4 - https://doi.org/10.2168/LMCS-11(4:18)2015A finer reduction of constraint problems to digraphsArticle
Authors: Jakub Bulín 
; Dejan Delic ; Marcel Jackson ; Todd Niven
It is well known that the constraint satisfaction problem over a general relational structure A is polynomial time equivalent to the constraint problem over some associated digraph. We present a variant of this construction and show that the corresponding constraint satisfaction problem is logspace equivalent to that over A. Moreover, we show that almost all of the commonly encountered polymorphism properties are held equivalently on the A and the constructed digraph. As a consequence, the Algebraic CSP dichotomy conjecture as well as the conjectures characterizing CSPs solvable in logspace and in nondeterministic logspace are equivalent to their restriction to digraphs.
Source: arXiv.org:1406.6413
Volume: Volume 11, Issue 4
Published on: December 29, 2015
Submitted on: June 25, 2014
Keywords: Computer Science - Computational Complexity,Computer Science - Logic in Computer Science,Mathematics - Combinatorics
Funding:
- Source : OpenAIRE Graph
- Structure of relations: algebra and applications; Code: FT120100666
- Funder: Natural Sciences and Engineering Research Council of Canada
- Complexity in Algebra and Algebra in Complexity: the role of finite semigroups and general algebra; Funder: Australian Research Council (ARC); Code: DP1094578
- Computation in direct powers; Funder: Australian Research Council (ARC); Code: P 24285
Classifications
Mathematics Subject Classification 20201
- 05C20 - Directed graphs (digraphs), tournaments
- 05C60 - Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)
- 08A35 - Automorphisms and endomorphisms of algebraic structures
- 68Q15 - Complexity classes (hierarchies, relations among complexity classes, etc.)
- 68R10 - Graph theory (including graph drawing) in computer science
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