Berthe Y. Choueiry

A new effcient algorithm for solving the simple temporal problem

In this paper we propose a new efficient algorithm, the STP-solver, for computing the minimal network of the Simple Temporal Problem (STP). This algorithm achieves high performance by exploiting a topological property of the constraint graph (i.e., triangulation) and a semantic property of the constraints (i.e., convexity) in light of the results reported by Bliek and Sam-Haroud [1], which were presented for general CSPs and have not yet been applied to temporal networks. Importantly, we design the constraint propagation in STP-solver to operate on triangles instead of operating on edges and implicitly guarantee the decomposition of the constraint graph according to its articulation points. We also provide extensive empirical evaluations of all known algorithms for solving the STP on sets of randomly generated problems. Our experiments demonstrate significant improvements of STPsolver, in terms of number of constraint checks and CPU time, over previously reported algorithms such as the Floyd-Warshall algorithm (F-W) [5; 8], Directed-Path Consistency (DPC) [8], and Partial Path-Consistency (PPC) [1].

Towards a practical theory of reformulation for reasoning about physical systems

In this paper, we provide a practical framework for characterizing, evaluating and selecting reformulation techniques for reasoning about physical systems, with the long-term goal of automating the selection and application of these techniques. We view reformulation as a mapping from one encoding of a problem to another. A problem solving task is in turn accomplished by the application of a sequence of reformulations to an initial problem encoding to produce a final encoding that addresses the task. Our framework provides the terminology to specify the conditions under which a particular reformulation technique is applicable, the cost associated with performing the reformulation, and the effects of the reformulation with respect to the problem encoding. As such it provides the vocabulary to characterize the selection of a sequence of reformulation techniques as a planning problem. Our framework is sufficiently flexible to accommodate previously proposed properties and metrics for reformulation. We have used the framework to characterize a variety of reformulation techniques, three of which are presented in this paper.

Dynamic Bundling: Less Effort for More Solutions

Bundling of the values of variables in a Constraint Satisfaction Problem (CSP) as the search proceeds is an abstraction mechanism that yields a compact representation of the solution space. We have previously established that, in spite of the effort of recomputing the bundles, dynamic bundling is never less effective than static bundling and nonbundling search strategies. Objections were raised that bundling mechanisms (whether static or dynamic) are too costly and not worthwhile when one is not seeking all solutions to the CSP. In this paper, we dispel these doubts and empirically show that (1) dynamic bundling remains superior in this context, (2) it does not require a full lookahead strategy, and (3) it dramatically reduces the cost of solving problems at the phase transition while yielding a bundle of multiple, robust solutions.

How the Level of Interchangeability Embedded in a Finite Constraint Satisfaction Problem Affects the Performance of Search

We investigate how the performance of search for solving finite constraint satisfaction problems (CSPs) is affected by the level of interchangeability embedded in the problem. First, we describe a generator of random CSPs that allows us to control the level of interchangeability in an instance. Then we study how the varying level of interchangeability affects the performance of search for finding one solution and all solutions to the CSP. We conduct experiments using forward-checking search, extended with static and dynamic ordering heuristics in combination with non-bundling, static, and dynamic bundling strategies. We demonstrate that: (1) While the performance of bundling decreases in general with decreasing interchangeability, this effect is muted when finding a first solution. (2) Dynamic ordering strategies are significantly more resistant to this degradation than static ordering. (3) Dynamic bundling strategies perform overall significantly better than static bundling strategies. Even when finding one solution, the size of the bundles yielded by dynamic bundling is large and less sensitive to the level of interchangeability. (4) The combination of dynamic ordering heuristics with dynamic bundling is advantageous. We conclude that this combination, in addition to yielding the best results, is the least sensitive to the level of interchangeability, and thus, indeed is superior to other searches.

On the Dynamic Detection of Interchangeability in Finite Constraint Satisfaction Problems

We investigate techniques that detect, dynamically during search, undeclared symmetries in the form of interchangeability (Freuder’91) in Constraint Satisfaction Problems, with the long-term goal of drawing a compact landscape of the solution space of a given CSP instance. As a first step towards our goal, we propose a new algorithm for dynamically computing interchangeability during backtrack search and demonstrate how it enhances the performance of search.

Revisiting Neighborhood Inverse Consistency on Binary CSPs

Our goal is to investigate the definition and application of strong consistency properties on the dual graphs of binary Constraint Satisfaction Problems (CSPs). As a first step in that direction, we study the structure of the dual graph of binary CSPs, and show how it can be arranged in a triangle-shaped grid. We then study, in this context, Relational Neighborhood Inverse Consistency (RNIC), which is a consistency property that we had introduced for non-binary CSPs [17]. We discuss how the structure of the dual graph of binary CSPs affects the consistency level enforced by RNIC. Then, we compare, both theoretically and empirically, RNIC to Neighborhood Inverse Consistency (NIC) and strong Conservative Dual Consistency (sCDC), which are higher-level consistency properties useful for solving difficult problem instances. We show that all three properties are pairwise incomparable.

Reformulating constraint satisfaction problems to improve scalability

Constraint Programming is a powerful approach for modeling and solving many combinatorial problems, scalability, however, remains an issue in practice. Abstraction and reformulation techniques are often sought to overcome the complexity barrier. In this paper we introduce four reformulation techniques that operate on the various components of a Constraint Satisfaction Problem (CSP) in order to reduce the cost of problem solving and facilitate scalability. Our reformulations modify one or more component of the CSP (i.e., the query, variables domains, constraints) and detect symmetrical solutions to avoid generating them. We describe each of these reformulations in the context of CSPs, then evaluate their performance and effects in on the building identification problem introduced by Michalowski and Knoblock.

Reformulating CSPs for scalability with application to geospatial reasoning

While many real-world combinatorial problems can be advantageously modeled and solved usingConstraint Programming, scalability remains a major issue in practice. Constraint models that accurately reflect the inherent structure of a problem, solvers that exploit the properties of this structure, and reformulation techniques that modify the problem encoding to reduce the cost of problem solving are typically used to overcome the complexity barrier. In this paper, we investigate such approaches in a geospatial reasoning task, the building-identification problem (BID), introduced and modeled as a Constraint Satisfaction Problem by Michalowski and Knoblock [1]. We introduce an improved constraint model, a custom solver for this problem, and a number of reformulation techniques that modify various aspects of the problem encoding to improve scalability. We show how interleaving these reformulations with the various stages of the solver allows us to solve much larger BID problems than was previously possible. Importantly, we describe the usefulness of our reformulations techniques for general Constraint Satisfaction Problems, beyond the BID application.

Constraint Processing Techniques for Improving Join Computation: A Proof of Concept

Constraint Processing and Database techniques overlap significantly. We discuss here the application of a constraint satisfaction technique, called dynamic bundling, to databases. We model the join query computation as a Constraint Satisfaction Problem (CSP) and solve it by search using dynamic bundling. First, we introduce a sort-based technique for computing dynamic bundling. Then, we describe the join algorithm that produces nested tuples. The resulting process yields a compact solution space and savings of memory, disk-space, and/or network bandwidth. We realize further savings by using bundling to reduce the number of join-condition checks. We place our bundling technique in the framework of the Progressive Merge Join (PMJ) [1] and use the XXL library [2] for implementing and testing our algorithm. PMJ assists in effective query-result-size prediction by producing early results. Our algorithm reinforces this feature of PMJ by producing the tuples as multiple solutions and is thus useful for improving size estimation.

Improving Relational Consistency Algorithms Using Dynamic Relation Partitioning

Relational consistency algorithms are instrumental for solving difficult instances of Constraint Satisfaction Problems (CSPs), often allowing backtrack-free search. In this paper, we improve an algorithm for enforcing relational consistency by exploiting the property that the constraints of the dual encoding of a CSP are piecewise functional. This property allows us to partition a CSP relation into blocks of equivalent tuples at varying levels of granularity. Our new algorithm dynamically exploits those partitions. Our experiments show a significant improvement of the processing time for enforcing relational consistency.