Eugene C. Freuder

The complexity of some polynomial network consistency algorithms for constraint satisfaction problems

Abstract Constraint satisfaction problems play a central role in artificial intelligence. A class of network consistency algorithms for eliminating local inconsistencies in such problems has previously been described. We analyze the time complexity of several node, arc and path consistency algorithms and prove that arc consistency is achievable in time linear in the number of binary constraints. The Waltz filtering algorithm is a special case of the arc consistency algorithm. In the edge labelling computational vision application the constraint graph is planar and so the time complexity is linear in the number of variables.

Synthesizing constraint expressions

A constraint network representation is presented for a combinatorial search problem: finding values for a set of variables subject to a set of constraints. A theory of consistency levels in such networks is formulated, which is related to problems of backtrack tree search efficiency. An algorithm is developed that can achieve any level of consistency desired, in order to preprocess the problem for subsequent backtrack search, or to function as an alternative to backtrack search by explicitly determining all solutions.

Contradicting Conventional Wisdom in Constraint Satisfaction

Constraint satisfaction problems have wide application in artificial intelligence. They involve finding values for problem variables where the values must be consistent in that they satisfy restrictions on which combinations of values are allowed. Two standard techniques used in solving such problems are backtrack search and consistency inference. Conventional wisdom in the constraint satisfaction community suggests: 1) using consistency inference as preprocessing before search to prune values from consideration reduces subsequent search effort and 2) using consistency inference during search to prune values from consideration is best done at the limited level embodied in the forward checking algorithm. We present evidence contradicting both pieces of conventional wisdom, and suggesting renewed consideration of an approach which fully maintains arc consistency during backtrack search.

A sufficient condition for backtrack-bounded search

Backtrack search is often used to solve constraint satisfaction problems. A relationship involving the structure of the constraints is described that provides a bound on the backtracking required to advance deeper into the backtrack tree. This analysis leads to upper bounds on the effort required for solution of a class of constraint satisfaction problems. The solutions involve a combination of relaxation preprocessing and backtrack search. The bounds are expressed in terms of the structure of the constraint connections. Specifically, the effort is shown to have a bound exponential in the size of the largest biconnected component of the constraint graph, as opposed to the size of the graph as a whole.

Understanding and improving the MAC algorithm

Constraint satisfaction problems have wide application in artificial intelligence. They involve finding values for problem variables where the values must be consistent in that they satisfy restrictions on which combinations of values are allowed. Recent research on finite domain constraint satisfaction problems suggest that Maintaining Arc Consistency (MAC) is the most efficient general CSP algorithm for solving large and hard problems. In the first part of this paper we explain why maintaining full, as opposed to limited, arc consistency during search can greatly reduce the search effort. Based on this explanation, in the second part of the paper we show how to modify MAC in order to make it even more efficient. Experimental results prove that the gain in efficiency can be quite important.

Stable Solutions for Dynamic Constraint Satisfaction Problems

An important extension of constraint technology involves problems that undergo changes that may invalidate the current solution. Previous work on dynamic problems sought methods for efficiently finding new solutions. We take a more proactive approach, exploring methods for finding solutions more likely to remain valid after changes that temporarily alter the set of valid assignments (stable solutions). To this end, we examine strategies for tracking changes in a problem and incorporating this information to guide search to solutions that are more likely to be stable. In this work search is carried out with a min-conflicts hill climbing procedure, and information about change is used to bias value selection, either by distorting the objective function or by imposing further criteria on selection. We study methods that track either value losses or constraint additions, and incorporate information about relative frequency of change into search. Our experiments show that these methods are generally effective in finding stable solutions, and in some cases handle the tradeoff between solution stability and search efficiency quite well. In addition, we identify one condition in which these methods markedly reduce the effort to find a stable solution.

Creating personalized documents: an optimization approach

The digital networked world is enabling and requiring a new emphasis on personalized document creation. The new, more dynamic digital environment demands tools that can reproduce both the contents and the layout automatically, tailored to personal needs and transformed for the presentation device, and can enable novices to easily create such documents. In order to achieve such automated document assembly and transformation, we have formalized custom document creation as a multiobjective optimization problem, and use a genetic algorithm to assemble and transform compound personalized documents. While we have found that such an automated process for document creation opens new possibilities and new workflows, we have also found several areas where further research would enable the approach to be more broadly and practically applied. This paper reviews the current system and outlines several areas where future research will broaden its current capabilities.

Constraints and AI planning

Tackling real-world planning problems often requires considering various types of constraints, which can range from simple numerical comparators to complex resources. This article provides an overview of techniques to deal with such constraints by expressing planning within general constraint-solving frameworks. Our goal here is to explore the interplay of constraints and planning, highlighting the differences between propositional satisfiability (SAT), integer programming (IP), and constraint programming (CP), and discuss their potential in expressing and solving AI planning problems.

In Pursuit of the Holy Grail

Constraint programming brings us closer to true declarative programming. Considerable progress has been made in this field; exciting challenges remain.

On forward checking for non-binary constraint satisfaction

Solving non-binary constraint satisfaction problems, a crucial challenge today, can be tackled in two different ways: translating the non-binary problem into an equivalent binary one, or extending binary search algorithms to solve directly the original problem. The latter option raises some issues when we want to extend definitions written for the binary case. This paper focuses on the well-known forward checking algorithm, and shows that it can be generalized to several non-binary versions, all fitting its binary definition. The classical non-binary version, proposed by Van Hentenryck, is only one of these generalizations.