A Dichotomy for 2-Constraint Forbidden CSP Patterns

TL;DR

This paper establishes a clear division in the complexity of certain CSP classes defined by forbidden patterns involving one or two constraints, leading to new tractable subclasses including a generalization of 2SAT.

Contribution

It provides a complete dichotomy for CSP classes defined by forbidden patterns with one or two constraints, identifying new tractable cases.

Findings

Established a dichotomy for forbidden pattern classes with one or two constraints.

Discovered new tractable classes, including a generalization of 2SAT.

Enhanced understanding of the structure of CSPs with forbidden subproblems.

Abstract

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.