Hybrid tractability of soft constraint problems

TL;DR

This paper explores hybrid conditions that guarantee the tractability of soft constraint problems, extending beyond traditional structural or constraint-type restrictions, and introduces new classes and tools like forbidden substructures.

Contribution

It introduces the concept of hybrid tractability for soft constraint problems and presents several novel classes that are efficiently solvable under these conditions.

Findings

Identified new hybrid classes of soft constraint problems

Included a machine scheduling problem as a tractable class

Developed the notion of forbidden substructures for analysis

Abstract

The constraint satisfaction problem (CSP) is a central generic problem in computer science and artificial intelligence: it provides a common framework for many theoretical problems as well as for many real-life applications. Soft constraint problems are a generalisation of the CSP which allow the user to model optimisation problems. Considerable effort has been made in identifying properties which ensure tractability in such problems. In this work, we initiate the study of hybrid tractability of soft constraint problems; that is, properties which guarantee tractability of the given soft constraint problem, but which do not depend only on the underlying structure of the instance (such as being tree-structured) or only on the types of soft constraints in the instance (such as submodularity). We present several novel hybrid classes of soft constraint problems, which include a machine scheduling problem, constraint problems of arbitrary arities with no overlapping nogoods, and the SoftAllDiff constraint with arbitrary unary soft constraints. An important tool in our investigation will be the notion of forbidden substructures.