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The power of arc consistency for CSPs defined by partially-ordered forbidden patterns

Abstract : Characterising tractable fragments of the constraint satisfaction problem (CSP) is an important challenge in theoretical computer science and arti ficial intelligence. Forbidding patterns (generic sub-instances) provides a means of defi ning CSP fragments which are neither exclusively language-based nor exclusively structure-based. It is known that the class of binary CSP instances in which the broken-triangle pattern (BTP) does not occur, a class which includes all tree-structured instances, are decided by arc consistency (AC), a ubiquitous reduction operation in constraint solvers. We provide a characterisation of simple partially-ordered forbidden patterns which have this AC-solvability property. It turns out that BTP is just one of fi ve such AC-solvable patterns. The four other patterns allow us to exhibit new tractable classes.
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Martin Cooper, Stanislav Živný. The power of arc consistency for CSPs defined by partially-ordered forbidden patterns. Logical Methods in Computer Science, Logical Methods in Computer Science Association, 2017, 13 (4:26), pp.1-32. ⟨10.23638/LMCS-13(4:26)2017⟩. ⟨hal-02640799⟩

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