Many AI synthesis problems such as planning, scheduling or design may be encoded in a constraint satisfaction problem (CSP). A CSP is typically defined as the problem of finding any consistent labeling for a fixed set of variables satisfying all given constraints between these variables. However, for many real tasks, the set of constraints to consider may evolve because of the environment or because of user interactions. The problem we consider here is the solution maintenance problem in such a dynamic CSP (DCSP). We propose a new class of constraint recording algorithms called Nogood Recording that may be used for solving both static and dynamic CSPs. It offers an interesting compromise, polynomially bounded in space, between an ATMS-like approach and the usual static constraint satisfaction algorithms. 1 Introduction The constraint satisfaction problem (CSP) model is widely used to represent and solve various AI related problems and provides fundamental tools in areas such as truth...

Learning during backtrack search is a space-intensive process that records information (such as additional constraints) in order to avoid redundant work. In this paper, we analyze the effects of polynomial-spacebounded learning on runtime complexity of backtrack search. One space-bounded learning scheme records only those constraints with limited size, and another records arbitrarily large constraints but deletes those that become irrelevant to the portion of the search space being explored. We find that relevance-bounded learning allows better runtime bounds than size-bounded learning on structurally restricted constraint satisfaction problems. Even when restricted to linear space, our relevancebounded learning algorithm has runtime complexity near that of unrestricted (exponential space-consuming) learning schemes.

4, and Toby Walsh 5

Search algorithms for solving CSP (Constraint Satisfaction Problems) usually fall into one of two main families: local search algorithms and systematic algorithms. Both families have their advantages. Designing hybrid approaches seems promising since those advantages may be combined into a single approach. In this paper, we present a new hybrid technique. It performs a local search over partial assignments instead of complete assignments, and uses filtering techniques and conflict-based techniques to efficiently guide the search. This new technique benefits from both classical approaches: aprioripruning of the search space from filtering-based search and possible repair of early mistakes from local search. We focus on a specific version of this technique: tabu decision-repair.Experiments done on open-shop scheduling problems show that our approach competes well with the best highly specialized algorithms. 2002 Elsevier Science B.V. All rights reserved.

The Constraint Satisfaction Problem is a type of combinatorial search problem of much interest in Artificial Intelligence and Operations Research. The simplest algorithm for solving such a problem is chronological backtracking, but this method suffers from a malady known as "thrashing," in which essentially the same subproblems end up being solved repeatedly. Intelligent backtracking algorithms, such as backjumping and dependency-directed backtracking, were designed to address this difficulty, but the exact utility and range of applicability of these techniques have not been fully explored. This dissertation describes an experimental and theoretical investigation into the power of these intelligent backtracking algorithms. We compare the empirical performance of several such algorithms on a range of problem distributions. We show that the more sophisticated algorithms are especially useful on those problems with a small number of constraints that happen to be difficult for chronologica...

Although the deep affinity between Graphplan's backward search, and the process of solving constraint satisfaction problems has been noted earlier, these relations have hither-to been primarily used to adapt CSP search techniques into the backward search phase of Graphplan. This paper describes GP-CSP, a system that does planning by automatically converting Graphplan's planning graph into a CSP encoding, and solving the CSP encoding using standard CSP solvers. Our comprehensive empirical evaluation of GP-CSP demonstrates that it is superior to both standard Graphplan and Blackbox system, which compiles planning graphs into SAT encodings. Our results show that CSP encodings outperform SAT encodings in terms of both space and time requirements. The space reduction is particularly important as it makes GP-CSP less susceptible to the memory blow-up associated with SAT compilation methods. Our work is inspired by the success of van Beek & Chen's CPLAN system. However, in contrast...

The paper compares two popular strategies for solving propositional satisfiability, backtracking search and resolution, and analyzes the complexity of a directional resolution algorithm (DR) as a function of the "width" (w) of the problem's graph.

Over the past few years, a new constraint-based formalism for temporal reasoning has been developed to represent and reason about Disjunctive Temporal Problems (DTPs). The class of DTPs is significantly more expressive than other problems previously studied in constraint-based temporal reasoning. In this paper we present a new algorithm for DTP solving, called Epilitis, which integrates strategies for efficient DTP solving from the previous literature, including conflict-directed backjumping, removal of subsumed variables, and semantic branching, and further adds no-good recording as a central technique. We discuss the theoretical and technical issues that arise in successfully integrating this range of strategies with one another and with no-good recording in the context of DTP solving. Using an implementation of Epilitis, we explore the effectiveness of various combinations of strategies for solving DTPs, and based on this analysis we demonstrate that Epilitis can achieve a nearly two order-of-magnitude speed-up over the previously published algorithms on benchmark problems in the DTP literature.

Recent work by Birnbaum & Lozinskii [1999] demonstrated that a clever yet simple extension of the well-known DavisPutnam procedure for solving instances of propositional satisfiability yields an efficient scheme for counting the number of satisfying assignments (models). We present a new extension, based on recursively identifying connected constraint-graph components, that substantially improves counting performance on random 3-SAT instances as well as benchmark instances from the SATLIB and Beijing suites. In addition, from a structure-based perspective of worst-case complexity, while polynomial time satisfiability checking is known to require only a backtrack search algorithm enhanced with nogood learning, we show that polynomial time counting using backtrack search requires an additional enhancement: good learning. Introduction Many practical problems from a variety of domains, most notably planning [Kautz & Selman 1996], have been efficiently solved by formulating ...

We report on the performance of an enhanced version of the "Davis-Putnam" (DP) proof procedure for propositional satisfiability (SAT) on large instances derived from realworld problems in planning, scheduling, and circuit diagnosis and synthesis. Our results show that incorporating CSP lookback techniques -- especially the relatively new technique of relevance-bounded learning -- renders easy many problems which otherwise are beyond DP's reach. Frequently they make DP, a systematic algorithm, perform as well or better than stochastic SAT algorithms such as GSAT or WSAT. We recommend that such techniques be included as options in implementations of DP, just as they are in systematic algorithms for the more general constraint satisfaction problem. Introduction While CNF propositional satisfiability (SAT) is a specific kind constraint satisfaction problem (CSP), until recently there has been little application of popular CSP look-back techniques in SAT algorithms. In previo...