scholarly journals Replaceability for Constraint Satisfaction Problems: Algorithms, Inference, and Complexity Patterns

10.29007/wrp9 ◽  
2018 ◽  
Author(s):  
Richard Wallace
Keyword(s):  
Constraint Satisfaction ◽  
Relative Effectiveness ◽  
Constraint Satisfaction Problems ◽  
Scheduling Problems ◽  
Problem Space ◽  
All Solutions ◽  
Disjunctive Constraints ◽  
Neighbourhood Search ◽  
Structured Problems ◽  
Full Search

Replaceability is a form of generalized substitutability whose features make it potentially of great importance for problem simplification. It differs from simple substitutability in that it only requires that substitutable values exist for every solution containing a given value without requiring that the former always be the same. This is the most general form of substitutability that allows inferences from local to global versions of this property. Building on earlier work, this study first establishes that algorithms for localized replaceability (consistent neighbourhood replaceability or CNR algorithms) based on all-solutions neighbourhood search outperform other replaceability algorithms by several orders of magnitude. It also examines the relative effectiveness of different forms of depth-first CNR algorithms. Secondly, it demonstrates an apparent complexity ridge, which does not occur at the same place in the problem space as the complexity areas for consistency or full search algorithms. Thirdly, it continues the study of methods for inferring replaceability in structured problems in order to improve efficiency. Here, it is shown that some strategies for inferring replaceable values can be extended to disjunctive constraints in scheduling problems.

scholarly journals Semantic Width and the Fixed-Parameter Tractability of Constraint Satisfaction Problems

2020 ◽  
Author(s):  
Hubie Chen ◽  
Georg Gottlob ◽  
Matthias Lanzinger ◽  
Reinhard Pichler
Keyword(s):  
Constraint Satisfaction ◽  
Fundamental Problem ◽  
Constraint Satisfaction Problems ◽  
Fixed Parameter Tractability ◽  
Scheduling Problems ◽  
Fixed Parameter Tractable ◽  
Database Theory ◽  
Formal Framework ◽  
Fixed Parameter

Constraint satisfaction problems (CSPs) are an important formal framework for the uniform treatment of various prominent AI tasks, e.g., coloring or scheduling problems. Solving CSPs is, in general, known to be NP-complete and fixed-parameter intractable when parameterized by their constraint scopes. We give a characterization of those classes of CSPs for which the problem becomes fixed-parameter tractable. Our characterization significantly increases the utility of the CSP framework by making it possible to decide the fixed-parameter tractability of problems via their CSP formulations. We further extend our characterization to the evaluation of unions of conjunctive queries, a fundamental problem in databases. Furthermore, we provide some new insight on the frontier of PTIME solvability of CSPs. In particular, we observe that bounded fractional hypertree width is more general than bounded hypertree width only for classes that exhibit a certain type of exponential growth. The presented work resolves a long-standing open problem and yields powerful new tools for complexity research in AI and database theory.

Reasoning about conditional constraint specification problems and feature models

2011 ◽  
Vol 25 (2) ◽  
pp. 163-174 ◽  
Author(s):  
Raphael Finkel ◽  
Barry O'Sullivan
Keyword(s):  
Constraint Satisfaction ◽  
Directed Acyclic Graphs ◽  
Constraint Satisfaction Problems ◽  
Product Configuration ◽  
Feature Models ◽  
Model Builder ◽  
A Value ◽  
Acyclic Graphs ◽  
All Solutions ◽  
Constraint Specification

AbstractProduct configuration is a major industrial application domain for constraint satisfaction techniques. Conditional constraint satisfaction problems (CCSPs) and feature models (FMs) have been developed to represent configuration problems in a natural way. CCSPs are like constraint satisfaction problems (CSPs), but they also include potential variables, which might or might not exist in any given solution, as well as classical variables, which are required to take a value in every solution. CCSPs model, for example, options on a car, for which the style of sunroof (a variable) only makes sense if the car has a sunroof at all. FMs are directed acyclic graphs of features with constraints on edges. FMs model, for example, cell phone features, where utility functions are required, but the particular utility function “games” is optional, but requires Java support. We show that existing techniques from formal methods and answer set programming can be used to naturally model CCSPs and FMs. We demonstrate configurators in both approaches. An advantage of these approaches is that the model builder does not have to reformulate the CCSP or FM into a classic CSP, converting potential variables into classical variables by adding a “does not exist” value and modifying the problem constraints. Our configurators automatically reason about the model itself, enumerating all solutions and discovering several kinds of model flaws.

scholarly journals The 2008 Classic Paper Award: Summary and Significance

AI Magazine ◽  
2010 ◽  
Vol 31 (4) ◽  
pp. 109
Author(s):  
Peter Friedland
Keyword(s):  
Local Search ◽  
Constraint Satisfaction ◽  
Wide Class ◽  
Large Scale ◽  
Constraint Satisfaction Problems ◽  
Paper Award ◽  
Scheduling Problems ◽  
Repair Method ◽  
Mark Johnston ◽  
Classic Paper

We at the NASA laboratory believed that our best work came when we simultaneously advanced AI theory and provided immediately usable solutions for current NASA problems. “Solving Large-Scale Constraint Satisfaction and Scheduling Problems Using a Heuristic Repair Method,” by Steve Minton, Mark Johnston, Andy Phillips, and Phil Laird clearly achieved both. It proved that local search and repair was applicable to a wide class of constraint satisfaction problems and clearly explicated the theory behind that proof.

scholarly journals A Hybrid Programming Framework for Modeling and Solving Constraint Satisfaction and Optimization Problems

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Paweł Sitek ◽  
Jarosław Wikarek
Keyword(s):  
Constraint Satisfaction ◽  
Optimization Problems ◽  
Solution Space ◽  
Original Method ◽  
Constraint Satisfaction Problems ◽  
Scheduling Problems ◽  
Hybrid Programming ◽  
Programming Framework ◽  
Autonomous Search ◽  
Constraint Optimization Problems

This paper proposes a hybrid programming framework for modeling and solving of constraint satisfaction problems (CSPs) and constraint optimization problems (COPs). Two paradigms, CLP (constraint logic programming) and MP (mathematical programming), are integrated in the framework. The integration is supplemented with the original method of problem transformation, used in the framework as a presolving method. The transformation substantially reduces the feasible solution space. The framework automatically generates CSP and COP models based on current values of data instances, questions asked by a user, and set of predicates and facts of the problem being modeled, which altogether constitute a knowledge database for the given problem. This dynamic generation of dedicated models, based on the knowledge base, together with the parameters changing externally, for example, the user’s questions, is the implementation of the autonomous search concept. The models are solved using the internal or external solvers integrated with the framework. The architecture of the framework as well as its implementation outline is also included in the paper. The effectiveness of the framework regarding the modeling and solution search is assessed through the illustrative examples relating to scheduling problems with additional constrained resources.

CONSTRAINT SATISFACTION PROBLEMS WITH ORDER-SORTED DOMAINS

1995 ◽  
Vol 04 (01n02) ◽  
pp. 55-72 ◽  
Author(s):  
TIBOR KÖKÉNY
Keyword(s):  
Constraint Satisfaction ◽  
Special Class ◽  
Object Oriented ◽  
Constraint Satisfaction Problems ◽  
Constraint Systems ◽  
Arc Consistency ◽  
All Solutions ◽  
Variable Domains ◽  
Natural Support ◽  
Inheritance Hierarchy

In order to improve constraint satisfaction techniques, a promising way is to use special features of constraints and variable domains. This paper examines a special class of CSPs (Constraint Satisfaction Problems) in which a partial order is defined on each domain and the constraints are compatible with these orders. A special arc-consistency algorithm for this case is presented and some questions about finding all solutions are discussed. The presented ideas can be used in constraint systems implemented in an object-oriented language, where inheritance hierarchy of objects is a natural support for the presented CSP type.

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