A Dichotomy for 2-Constraint Forbidden CSP Patterns
This work addresses the challenge of identifying tractable CSP instances for researchers in computational complexity, though it appears incremental as it builds on prior pattern-based approaches.
The authors tackled the problem of characterizing tractable classes of constraint satisfaction problems (CSPs) by forbidding patterns, and they established a dichotomy for patterns with one or two constraints, leading to the discovery of new tractable classes such as a generalization of 2SAT.
Although the CSP (constraint satisfaction problem) is NP-complete, even in the case when all constraints are binary, certain classes of instances are tractable. We study classes of instances defined by excluding subproblems. This approach has recently led to the discovery of novel tractable classes. The complete characterisation of all tractable classes defined by forbidding patterns (where a pattern is simply a compact representation of a set of subproblems) is a challenging problem. We demonstrate a dichotomy in the case of forbidden patterns consisting of either one or two constraints. This has allowed us to discover new tractable classes including, for example, a novel generalisation of 2SAT.