Super-Reparametrizations of Weighted CSPs: Properties and Optimization Perspective

TL;DR

This paper explores super-reparametrizations of Weighted CSPs, revealing their theoretical properties, and introduces a framework for using them to compute improved upper bounds on WCSP solutions, demonstrated through experiments.

Contribution

It provides the first detailed study of super-reparametrizations and develops a new framework for bounding WCSP solutions using these transformations.

Findings

Super-reparametrizations can improve bounds on WCSPs.

The framework generalizes existing constraint propagation methods.

SAC-based bounds outperform other local consistencies on benchmarks.

Abstract

The notion of reparametrizations of Weighted CSPs (WCSPs) (also known as equivalence-preserving transformations of WCSPs) is well-known and finds its use in many algorithms to approximate or bound the optimal WCSP value. In contrast, the concept of super-reparametrizations (which are changes of the weights that keep or increase the WCSP objective for every assignment) was already proposed but never studied in detail. To fill this gap, we present a number of theoretical properties of super-reparametrizations and compare them to those of reparametrizations. Furthermore, we propose a framework for computing upper bounds on the optimal value of the (maximization version of) WCSP using super-reparametrizations. We show that it is in principle possible to employ arbitrary (under some technical conditions) constraint propagation rules to improve the bound. For arc consistency in particular, the method reduces to the known Virtual AC (VAC) algorithm. We implemented the method for singleton arc consistency (SAC) and compared it to other strong local consistencies in WCSPs on a public benchmark. The results show that the bounds obtained from SAC are superior for many instance groups.