Exploiting the Structure of Constraint Satisfaction Problems by Interchangeability (original) (raw)

Interchangeability in constraint satisfaction problems

2004

Combinatorial optimization is a powerful paradigm for representing complex problems. It has a wide range of applications such as planning, scheduling, resource sharing, in many domains such as transportation, production, mass marketing, network management, human resources management. Constraint satisfaction techniques provide efficient algorithms to prune search spaces.

Studying Interchangeability in Constraint Satisfaction Problems

Lecture Notes in Computer Science, 2002

Enumerating all Solutions for Constraint Satisfaction Problems

2006

Constraint satisfaction problems are generalizations of many combinatorial problems. In recent years, there have been many results on the complexity of this problem, and it has proven to be interesting both from a practical and from a theoretical point of view. We study the corresponding enumeration problem, and present new efficient algorithms which enumerate, for a given CSP-formula, the set of its solutions. Such algorithms exist for a broad class of constraint languages on arbitrary finite domains. We also show that the algebraic techniques usually applied in the constraint satisfaction context do not work for the enumeration problem.

Tractability in constraint satisfaction problems: a survey

Constraints, 2015

Even though the Constraint Satisfaction Problem (CSP) is NP-complete, many tractable classes of CSP instances have been identified. After discussing different forms and uses of tractability, we describe some landmark tractable classes and survey recent theoretical results. Although we concentrate on the classical CSP, we also cover its important extensions to infinite domains and optimisation, as well as #CSP and QCSP. 1. automatic recognition and resolution of easy instances within general-purpose solvers, supported by ANR Project ANR-10-BLAN-0210 and EPSRC grant EP/L021226/1.

Solution Techniques for Constraint Satisfaction Problems: Foundations

Artificial Intelligence Review, 2001

Conventional techniques for the constraint satisfaction problem (CSP) have had considerable success in their applications. However, there are many areas in which the performance of the basic approaches may be improved. These include heuristic ordering of certain tasks performed by the CSP solver, hybrids which combine compatible solution techniques and graph based methods which exploit the structure of the constraint graph representation of a CSP. Also, conventional constraint satisfaction techniques only address problems with hard constraints (i.e. each of which are completely satisfied or completely violated, and all of which must be satisfied by a valid solution). Many real applications require a more flexible approach which relaxes somewhat these rigid requirements. To address these issues various approaches have been developed. This paper attempts a systematic review of them.

Structural tractability of enumerating CSP solutions

Constraints, 2013

The problem of deciding whether CSP instances admit solutions has been deeply studied in the literature, and several structural tractability results have been derived so far. However, constraint satisfaction comes in practice as a computation problem where the focus is either on finding one solution, or on enumerating all solutions, possibly projected to some given set of output variables. The paper investigates the structural tractability of the problem of enumerating (possibly projected) solutions, where tractability means here computable with polynomial delay (WPD), since in general exponentially many solutions may be computed. A general framework based on the notion of tree projection of hypergraphs is considered, which generalizes all known decomposition methods. Tractability results have been obtained both for classes of structures where output variables are part of their specification, and for classes of structures where computability WPD must be ensured for any possible set of output variables. These results are shown to be tight, by exhibiting dichotomies for classes of structures having bounded arity and where the tree decomposition method is considered.

A Definition of Interchangeability for Soft CSPs

Substitutability and interchangeability in constraint satisfaction problems (CSPs) have been used as a basis for search heuristics, solution adaptation and abstraction techniques. In this paper, we consider how the same concepts can be extended to soft constraint satisfaction problems (SCSPs). We introduce two notions: threshold α and degradation δ for substitutability and interchangeability, ( α substitutability/interchangeability and δ substitutability/interchangeability respectively). We show that they satisfy analogous theorems to the ones already known for hard constraints. In α interchangeability, values are interchangeable in any solution that is better than a threshold α, thus allowing to disregard differences among solutions that are not sufficiently good anyway. In δ interchangeability, values are interchangeable if their exchange could not degrade the solution by more than a factor of δ. We give efficient algorithms to compute ( δ /α)interchangeable sets of value for a large class of SCSPs. standard paper