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Combining Treewidth and Backdoors for CSP

Authors Robert Ganian, M. S. Ramanujan, Stefan Szeider

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Robert Ganian
M. S. Ramanujan
Stefan Szeider

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Robert Ganian, M. S. Ramanujan, and Stefan Szeider. Combining Treewidth and Backdoors for CSP. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 36:1-36:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.STACS.2017.36

Abstract

We show that CSP is fixed-parameter tractable when parameterized by the treewidth of a backdoor into any tractable CSP problem over a finite constraint language. This result combines the two prominent approaches for achieving tractability for CSP: (i) structural restrictions on the interaction between the variables and the constraints and (ii) language restrictions on the relations that can be used inside the constraints. Apart from defining the notion of backdoor-treewidth and showing how backdoors of small treewidth can be used to efficiently solve CSP, our main technical contribution is a fixed-parameter algorithm that finds a backdoor of small treewidth.
Keywords
  • Algorithms and data structures
  • Fixed Parameter Tractability
  • Constraint Satisfaction

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