Chavalit Likitvivatanavong

A path-optimal GAC algorithm for table constraints

Filtering 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.

Computing explanations and implications in preference-based configurators

We consider configuration problems with preferences rather than just hard constraints, and we analyze and discuss the features that such configurators should have. In particular, these configurators should provide explanations for the current state, implications of a future choice, and also information about the quality of future solutions, all with the aim of guiding the user in the process of making the right choices to obtain a good solution. We then describe our implemented system, which, by taking the soft n-queens problem as an example, shows that it is indeed possible, even in this very general context of preference-based configurators, to automatically compute all the information needed for the desired features. This is done by keeping track of the inferences that are made during the constraint propagation enforcing phases.

Deriving Explanations and Implications for Constraint Satisfaction Problems

We explore the problem of deriving explanations and implications for constraint satisfaction problems (CSPs). We show that consistency methods can be used to generate inferences that support both functions. Explanations take the form of trees that showthe basis for assignments and deletions in terms of previous selections. These ideas are illustrated by dynamic, interactive testbeds.

Eliminating redundancy in CSPs through merging and subsumption of domain values

Onto-substitutability has been shown to be intrinsic to how a domain value is considered redundant in Constraint Satisfaction Problems (CSPs). A value is onto-substitutable if any solution involving that value remains a solution when that value is replaced by some other value. We redefine onto-substitutability to accommodate binary relationships and study its implication. Joint interchangeability, an extension of onto-substitutability to its interchangeability counterpart, emerges as one of the results. We propose a new way of removing interchangeable values by constructing a new value as an intermediate step, as well as introduce virtual interchangeability, a local reasoning that leads to joint interchangeability and allows values to be merged together. Algorithms for removing onto-substitutable values are also proposed.

STR3: A path-optimal filtering algorithm for table constraints☆

Abstract Constraint propagation is a key to the success of Constraint Programming (CP). The principle is that filtering algorithms associated with constraints are executed in sequence until quiescence is reached. Many such algorithms have been proposed over the years to enforce the property called Generalized Arc Consistency (GAC) on many types of constraints, including table constraints that are defined extensionally. Recent advances in GAC algorithms for extensional constraints rely on directly manipulating tables during search. This is the case with a simple approach called Simple Tabular Reduction (STR), which systematically maintains tables of constraints to their relevant lists of tuples. In particular, STR2, a refined STR variant is among the most efficient GAC algorithms for positive table constraints. In this paper, we revisit this approach by proposing a new GAC algorithm called STR3 that is specifically designed to enforce GAC during backtrack search. By indexing tables and reasoning from deleted values, we show that STR3 can avoid systematically iterating over the full set of current tuples, contrary to STR2. An important property of STR3 is that it can completely avoid unnecessary traversal of tables, making it optimal along any path of the search tree. We also study a variant of STR3, based on an optimal circular way for traversing tables, and discuss the relationship of STR3 with two other optimal GAC algorithms introduced in the literature, namely, GAC4 and AC5TC-Tr. Finally, we demonstrate experimentally how STR3 is competitive with the state-of-the-art. In particular, our extensive experiments show that STR3 is generally faster than STR2 when the average size of tables is not reduced too drastically during search, making STR3 complementary to STR2.

Higher-Order Consistencies through GAC on Factor Variables

Filtering constraint networks to reduce search space is one of the main cornerstones of Constraint Programming and among them (Generalized) Arc Consistency has been the most fundamental. While stronger consistencies are also the subject of considerable attention, none matches GAC’s and for this reason it continues to advance at a steady pace and has become the popular choice of consistency for filtering algorithms. In this paper, we build on the success of GAC by proposing a way to transform a constraint network into another such that enforcing GAC on the latter is equivalent to enforcing a stronger consistency on the former. The key idea is to factor out commonly shared variables from constraints’ scopes, form new variables, then re-attach them back to the constraints where they come from. Experiments show that this method is inexpensive and outperforms specialized algorithms and other techniques when it comes to full pair-wise consistency (FPWC).

A Refutation Approach to Neighborhood Interchangeability in CSPs

The concept of Interchangeability was developed to deal with redundancy of values in the same domain. Conventional algorithms for detecting Neighborhood Interchangeability work by gradually establishing relationships between values from scratch. We propose the opposite strategy: start by assuming everything is interchangeable and disprove certain relations as more information arises. Our refutation-based algorithms have much better lower bounds whereas the lower bound and the upper bound of the traditional algorithms are asymptotically identical.

Many-to-many interchangeable sets of values in CSPs

Onto-substitutability has been shown to be intrinsic to how a domain value is considered redundant. A value is onto-substitutable if any solution involving that value remains a solution when that value is replaced by some other value. We redefine onto-substitutability to accommodate binary relationships and study its implication. Joint interchangeability, an extension of onto-substitutability to its interchangeability counterpart, emerges as one of the results. We propose a new way of removing interchangeable values by constructing a new value as an intermediate step, as well as introduce virtual interchangeability, a local reasoning that leads to joint interchangeability and allows values to be merged together.

Improving the lower bound of simple tabular reduction

Simple Tabular Reduction (STR) is a state-of-the-art filtering technique for enforcing Generalized Arc Consistency (GAC) on positive table constraints. Despite its good performance in practice, the STR2 algorithm suffers from a mandatory lower bound equal to the number of domain values in the current state of the problem, because the presence of each value must be justified every time STR2 is called. We overcome this fixed cost by redesigning STR2 and incorporating watched tuples. Experiments show that the revised algorithm is better at coping with problems that involve a large number of small changes during search and it can be more than twice as fast on certain structured problems.

Extracting microstructure in binary constraint networks

We present algorithms that perform the extraction of partial assignments from binary Constraint Satisfaction Problems without introducing new constraints. They are based on a new perspective on domain values: we view a value not as a single, indivisible unit, but as a combination of value fragments. Applications include removing nogoods while maintaining constraint arity, learning nogoods in the constraint network, enforcing on neighborhood inverse consistency and removal of unsolvable sub-problems from the constraint network.