Consistency and Random Constraint Satisfaction Models

TL;DR

This paper introduces a flexible framework for designing random constraint satisfaction problems (CSPs) that exhibit phase transitions and high complexity by leveraging the concept of constraint consistency, with experimental validation.

Contribution

The paper presents a novel, adaptable framework for creating random CSP models that incorporate structural elements and constraint consistency to achieve interesting computational behaviors.

Findings

Models exhibit phase transition phenomena.

Structural elements improve problem hardness.

Backtracking algorithms are affected by model features.

Abstract

In this paper, we study the possibility of designing non-trivial random CSP models by exploiting the intrinsic connection between structures and typical-case hardness. We show that constraint consistency, a notion that has been developed to improve the efficiency of CSP algorithms, is in fact the key to the design of random CSP models that have interesting phase transition behavior and guaranteed exponential resolution complexity without putting much restriction on the parameter of constraint tightness or the domain size of the problem. We propose a very flexible framework for constructing problem instances withinteresting behavior and develop a variety of concrete methods to construct specific random CSP models that enforce different levels of constraint consistency. A series of experimental studies with interesting observations are carried out to illustrate the effectiveness of introducing structural elements in random instances, to verify the robustness of our proposal, and to investigate features of some specific models based on our framework that are highly related to the behavior of backtracking search algorithms.