scholarly journals Variable Elimination in Binary CSPs

2019 ◽  
Vol 66 ◽  
pp. 589-624
Author(s):  
Martin C. Cooper ◽  
Achref El Mouelhi ◽  
Cyril Terrioux
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
Benchmark Problems ◽  
Study Variable ◽  
Variable Elimination ◽  
Problem Instances ◽  
Forbidden Patterns

We investigate rules which allow variable elimination in binary CSP (constraint satisfaction problem) instances while conserving satisfiability. We study variable-elimination rules based on the language of forbidden patterns enriched with counting and quantification over variables and values. We propose new rules and compare them, both theoretically and experimentally. We give optimised algorithms to apply these rules and show that each define a novel tractable class. Using our variable-elimination rules in preprocessing allowed us to solve more benchmark problems than without.

scholarly journals Variable Elimination in Binary CSPs (Extended Abstract)

2020 ◽  
Author(s):  
Martin C. Cooper ◽  
Achref El Mouelhi ◽  
Cyril Terrioux
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
Benchmark Problems ◽  
Variable Elimination ◽  
Problem Instances

We investigate rules which allow variable elimination in binary CSP (constraint satisfaction problem) instances while conserving satisfiability. We propose new rules and compare them, both theoretically and experimentally. We give optimised algorithms to apply these rules and show that each defines a novel tractable class. Using our variable-elimination rules in preprocessing allowed us to solve more benchmark problems than without.

scholarly journals Galois Connections for Patterns: An Algebra of Labelled Graphs

2021 ◽  
pp. 125-150
Author(s):  
David A. Cohen ◽  
Martin C. Cooper ◽  
Peter G. Jeavons ◽  
Stanislav Živný
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
Galois Connection ◽  
Language Classes ◽  
Finite Set ◽  
Binary Constraint ◽  
Tree Width ◽  
To Come ◽  
Forbidden Patterns ◽  
Near Unanimity

AbstractA pattern is a generic instance of a binary constraint satisfaction problem (CSP) in which the compatibility of certain pairs of variable-value assignments may be unspecified. The notion of forbidden pattern has led to the discovery of several novel tractable classes for the CSP. However, for this field to come of age it is time for a theoretical study of the algebra of patterns. We present a Galois connection between lattices composed of sets of forbidden patterns and sets of generic instances, and investigate its consequences. We then extend patterns to augmented patterns and exhibit a similar Galois connection. Augmented patterns are a more powerful language than flat (i.e. non-augmented) patterns, as we demonstrate by showing that, for any $$k \ge 1$$ k ≥ 1 , instances with tree-width bounded by k cannot be specified by forbidding a finite set of flat patterns but can be specified by a finite set of augmented patterns. A single finite set of augmented patterns can also describe the class of instances such that each instance has a weak near-unanimity polymorphism of arity k (thus covering all tractable language classes).We investigate the power of forbidding augmented patterns and discuss their potential for describing new tractable classes.

scholarly journals Planning Graph as a (Dynamic) CSP: Exploiting EBL, DDB and other CSP Search Techniques in Graphplan

2000 ◽  
Vol 12 ◽  
pp. 1-34 ◽  
Author(s):  
S. Kambhampati
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
Benchmark Problems ◽  
Dynamic Variable ◽  
Search Techniques ◽  
Variable Ordering ◽  
Dynamic Constraint ◽  
Explanation Based Learning ◽  
Planning Graph ◽  
Random Restart

This paper reviews the connections between Graphplan's planning-graph and the dynamic constraint satisfaction problem and motivates the need for adapting CSP search techniques to the Graphplan algorithm. It then describes how explanation based learning, dependency directed backtracking, dynamic variable ordering, forward checking, sticky values and random-restart search strategies can be adapted to Graphplan. Empirical results are provided to demonstrate that these augmentations improve Graphplan's performance significantly (up to 1000x speedups) on several benchmark problems. Special attention is paid to the explanation-based learning and dependency directed backtracking techniques as they are empirically found to be most useful in improving the performance of Graphplan.

scholarly journals The Tractability of CSP Classes Defined by Forbidden Patterns

2012 ◽  
Vol 45 ◽  
pp. 47-78 ◽  
Author(s):  
D. A. Cohen ◽  
M. C. Cooper ◽  
P. Creed ◽  
D. Marx ◽  
A. Z. Salamon
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
The Novel ◽  
Considerable Effort ◽  
Relational Properties ◽  
Np Complete ◽  
Novel Concept ◽  
Forbidden Patterns ◽  
Special Case ◽  
Hybrid Properties

The constraint satisfaction problem (CSP) is a general problem central to computer science and artificial intelligence. Although the CSP is NP-hard in general, considerable effort has been spent on identifying tractable subclasses. The main two approaches consider structural properties (restrictions on the hypergraph of constraint scopes) and relational properties (restrictions on the language of constraint relations). Recently, some authors have considered hybrid properties that restrict the constraint hypergraph and the relations simultaneously. Our key contribution is the novel concept of a CSP pattern and classes of problems defined by forbidden patterns (which can be viewed as forbidding generic sub-problems). We describe the theoretical framework which can be used to reason about classes of problems defined by forbidden patterns. We show that this framework generalises certain known hybrid tractable classes. Although we are not close to obtaining a complete characterisation concerning the tractability of general forbidden patterns, we prove a dichotomy in a special case: classes of problems that arise when we can only forbid binary negative patterns (generic sub-problems in which only disallowed tuples are specified). In this case we show that all (finite sets of) forbidden patterns define either polynomial-time solvable or NP-complete classes of instances.

Sign in / Sign up

Export Citation Format

Share Document