A Probabilistic-Based Model for Binary CSP

TL;DR

This paper presents a probabilistic model for binary constraint satisfaction problems (CSP) that predicts domain inconsistencies and provides bounds, along with a polynomial-time algorithm for propagating this probabilistic information.

Contribution

It introduces a novel probabilistic framework for analyzing binary CSPs, including bounds and an efficient propagation algorithm.

Findings

Predicts the probability of domain value inconsistency.

Provides bounds for probabilistic indicators.

Includes a polynomial-time propagation algorithm.

Abstract

This work introduces a probabilistic-based model for binary CSP that provides a fine grained analysis of its internal structure. Assuming that a domain modification could occur in the CSP, it shows how to express, in a predictive way, the probability that a domain value becomes inconsistent, then it express the expectation of the number of arc-inconsistent values in each domain of the constraint network. Thus, it express the expectation of the number of arc-inconsistent values for the whole constraint network. Next, it provides bounds for each of these three probabilistic indicators. Finally, a polytime algorithm, which propagates the probabilistic information, is presented.