Extended Formulation for CSP that is Compact for Instances of Bounded Treewidth

TL;DR

This paper introduces a compact extended formulation for constraint satisfaction problems on graphs with bounded treewidth, leading to improved upper bounds on the extension complexity of related NP-hard problems.

Contribution

It presents a polynomial-sized extended formulation for CSPs with bounded treewidth, advancing understanding of their computational complexity.

Findings

Extended formulation size is polynomial for bounded treewidth instances.

New upper bounds on extension complexity for NP-hard problems on such graphs.

Implications for solving CSPs more efficiently in specific graph classes.

Abstract

In this paper we provide an extended formulation for the class of constraint satisfaction problems and prove that its size is polynomial for instances whose constraint graph has bounded treewidth. This implies new upper bounds on extension complexity of several important NP-hard problems on graphs of bounded treewidth.