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.
Highlights
Many important combinatorial optimization problems belong to the class of constraint satisfaction problems (CSP)
A lot of attention has been given to study extension complexity of problems [6]: given a problem Q, what is the minimum number of inequalities representing a polytope whose linear projection coincides with the convex hull H of all integral solutions of Q? Any polytope which projects to H is called an extended formulation of H
We present an extended formulation for CSP and show that its size is polynomial for instances of CSP whose constraint graph has bounded treewidth
Summary
Many important combinatorial optimization problems belong to the class of constraint satisfaction problems (CSP). It has been shown that CSP is solvable in polynomial time for instances whose constraint graph has bounded treewidth [8]. Any polytope which projects to H is called an extended formulation of H. Note that membership of a problem in the class P of polynomially solvable problems does not necessarily imply the existence of an extended formulation of polynomial size [18]. We present an extended formulation for CSP and show that its size is polynomial for instances of CSP whose constraint graph has bounded treewidth
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