Maintaining Arc Consistency with Multiple Residues

International audienceExploiting residual supports (or residues) has proved to be one of the most cost-effective approaches for Maintaining Arc Consistency during search (MAC). While MAC based on optimal AC algorithm may have better theoretical time complexity in some cases, in practice the overhead for maintaining required data structure during search outweighs the benefit, not to mention themore complicated implementation. Implementing MAC with residues, on the other hand, is trivial. In this paper we extend previous work on residues and investigate the use of multiple residues during search. We first give a theoretical analysis of residue-based algorithms that explains their good practical performance. We then propose several heuristics on how to deal with multiple residues. Finally, our empirical study shows that with a proper and limited number of residues, many constraint checks can be saved. When the constraint check is expensive or a problem is hard, the multiple residues approach is competitive in both the number of constraint checks and cpu time

Domain value mutation and other techniques for constraint satisfaction problems

The term Constraint Satisfaction Problem (CSP) refers to a class of NP-complete problems, a collection of difficult problems for which no fast solution is known. The standard definition of a CSP involves variables, values, and constraints: each variable must be assigned a value from a designated group of possible values (also known as the variable’s domain), while a constraint on a set of variables indicates permissible combinations of values for these variables. Given a CSP, an important objective is to query whether it has a solution — an assignment of each variable to a value such that all constraints are satisfied. Solving a CSP usually requires chronological backtracking search that interleaves variable assignments with various kinds of inferences in order to reduce the search space. This dissertation comprises two parts. The first part deals with a modification of the classical CSP model that allows a value to be broken up and multiple values to be combined. The second part deals with generalized arc consistency algorithms. Both parts share a common theme in that extensional constraints --‐ the most basic expression possible for constraints --- play the central role. Despite being an important class, extensional constraints have received much less attention recently as most efforts have been channelled toward identifying new types of specialized constraints and coming up with corresponding algorithms. Regardless, improvements to algorithms for extensional constraints are more fundamental. This dissertation will attempt to improve existing techniques and algorithms for extensional constraints by examining them critically from the bottom up and approaching them from a novel direction

Splitting the atom: A new approach to Neighbourhood Interchangeability in Constraint Satisfaction Problems

We investigate interchangeability of values in CSPs, based on an approach where a single value in the domain of a variable can be treated as a combination of “sub-values”. An algorithm for removing overlapping sub-values is presented. The resulting CSPs take less time to find all solutions and yield a more compactly-representable, but equivalent, solution set. Experimental results show that, especially in loose problems with large numbers of solutions, dramatic savings in search cost are achieved.

Question-Generation In Constraint-Based Expert Systems

If-then rules are the core knowledge representation technology in currently deployed expert systems. However, if we replace rules by constraints, we can greatly extend both the expressive and reasoning functionality of such systems. An open issue, however, is how best should constraint-based expert systems decide which questions to ask their users during a consultation -- how can an interactive constraint-based expert system extract needed data from its users while imposing the smallest possible burden on those users. In this paper we consider three types of approach to the task

A path-optimal GAC algorithm for table constraints

International audienceFiltering by Generalized Arc Consistency (GAC) is a fundamental technique in Constraint Programming. Recent advances in GAC algorithms for extensional constraints rely on direct manipulation of tables during search. Simple Tabular Reduction (STR), which systematically removes invalid tuples from tables, has been shown to be a simple yet efficient approach. STR2, a refinement of STR, is considered to be among the best filtering algorithms for positive table constraints. In this paper, we introduce a new GAC algorithm called STR3 that is specifically designed to enforce GAC during search. STR3 can completely avoid unnecessary traversal of tables, making it optimal along any path of the search tree. Our experiments show that STR3 is much faster than STR2 when the average size of the tables is not reduced drastically during search

STR3: A path-optimal filtering algorithm for table constraints

10.1016/j.artint.2014.12.002Artificial Intelligence2201-2