Phase Transition of Tractability in Constraint Satisfaction and Bayesian Network Inference

TL;DR

This paper investigates the phase transition in the tractability of constraint satisfaction and Bayesian network inference problems, showing that bounded treewidth leads to a sharp change in problem complexity even in sparse structures.

Contribution

It identifies a phase transition in the treewidth of random CSPs and Bayesian networks, revealing limits of treewidth-based algorithms in random instances.

Findings

Phase transition occurs while structures are still sparse.

Treewidth-based algorithms are only effective in a limited range.

Tractability is linked to the structural property of treewidth.

Abstract

There has been great interest in identifying tractable subclasses of NP complete problems and designing efficient algorithms for these tractable classes. Constraint satisfaction and Bayesian network inference are two examples of such problems that are of great importance in AI and algorithms. In this paper we study, under the frameworks of random constraint satisfaction problems and random Bayesian networks, a typical tractable subclass characterized by the treewidth of the problems. We show that the property of having a bounded treewidth for CSPs and Bayesian network inference problem has a phase transition that occurs while the underlying structures of problems are still sparse. This implies that algorithms making use of treewidth based structural knowledge only work efficiently in a limited range of random instance.