A theoretical evaluation of selected backtracking algorithms (original) (raw)
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Backtracking Algorithms for Constraint Satisfaction Problems
1999
Over the past twenty five years many backtracking algorithms havebeen developed for constraint satisfaction problems. This survey describesthe basic backtrack search within the search space framework and thenpresents a number of improvements developed in the past two decades,including look-back methods such as backjumping, constraint recording,backmarking, and look-ahead methods such as forward checking and dynamicvariable ordering.1 IntroductionConstraint networks have proven...
A bit of history ... Constraints have recently emerged as a research area that combines researchers from a number of fields, including Artificial Intelligence, Programming Languages, Symbolic Computing and Computational Logic. Constraint networks and constraint satisfaction problems have been studied in Artificial Intelligence starting from the seventies (Montanary, 1974), (Waltz, 1975). Systematic use of constraints in programming has started in the eighties (Gallaire, 1985), (Jaffar, Lassez, 1987). The constraint satisfaction origins from Artificial Intelligence where the problems like scene labelling was studied (Waltz, 1975). The scene labelling problem is probably the first constraint satisfaction problem that was formalised. The goal is to recognise the objects in the scene by interpreting lines in the drawings. First, the lines or edges are labelled, i.e., they are categorised into few types, namely convex (+), concave (-) and occluding edges (<). In some advanced systems, the shadow border is recognised as well. There are a lot ways how to label the scene (exactly 3 n , where n is a number of edges) but only few of them has any 3D meaning. The idea how to solve this combinatorial problem is to find legal labels for junctions satisfying the constraint that the edge has the same label at both ends. This reduces the problem a lot because there are only a very limited number of legal labels for junctions. ... and some applications. Constraint programming has been successfully applied in numerous domains. Recent applications include computer graphics (to express geometric coherence in the case of scene analysis), natural language processing (construction of efficient parsers), database systems (to ensure and/or restore consistency of the data), operations research problems (like optimisation problems), molecular biology (DNA sequencing), business applications (option trading), electrical engineering (to locate faults), circuit design (to compute layouts), etc. Current research in this area deals with various foundational issues, with implementation aspects, and with new applications of constraint programming. What does the constraint programming deal with? Constraint programming is the study of computational systems based on constraints. The idea of constraint programming is to solve problems by stating constraints (conditions, properties, requirements) which must be satisfied by the solution.
Dynamic Backtracking with Constraint Propagation
Recent w orks on constraint relaxation ] provided the decorum system (Deduction-based Constraint Relaxation Management). In this paper, we show h o w the ideas developed in that system can be used in order to integrate Constraint Propagation within the Dynamic Backtracking algorithm . Dynamic Backtracking replaces the backtracking process by a m uch less blind behavior that consists in local modi cations of the choices made up to the current situation. Thus the whole constraint programming community m a y derive bene ts from its integration with a constraint propagation algorithm.
Hybrid algorithms for the constraint satisfaction problem
2007
It might be said that there are five basic tree search algorithms for the constraint satisfaction problem (csp), namely, naive backtracking (BT), backjumping (BJ), conflict-directed backjumping (CBJ), backmarking (BM), and forward checking (FC). In broad terms, BT, BJ, and CBJ describe different styles of backward move (backtracking), whereas BT, BM, and FC describe different styles of forward move (labeling of variables). This paper presents an approach that allows base algorithms to be combined, giving us new hybrids.
Increasing Tree Search Efficiency for Constraint Satisfaction Problems
Artificial Intelligence, 1980
In this paper we explore the number of tree search operations required to solve binary constraint satisfaction problems. We show analytically and experimentally that the two principles of first trying the places most likely to fail and remembering what has been done to avoid repeating the same mistake twice improve the standard backtracking search. We experimentally show that a lookahead procedure called forward checking (to anticipate the future) which employs the most likely to fail principle performs better than standard backtracking, Ullman's, Waltz's, Mackworth's, and Haralick's discrete relaxation in all cases tested, and better than Gaschnig's backmarking in the larger problems.
Algorithms for Constraint Satisfaction Problems (CSPs
Many problems in AI can be modeled as constraint satisfaction problems (CSPs). Hence the development of e ective solution techniques for CSPs is an important research problem. Forward checking (FC) with some other heuristics has been traditionally considered to be the best algorithm for solving CSPs while recently there have been a number of claims that maintaining arc consistency (MAC) is more e cient on large and hard CSPs. In this thesis, we p r o vide a systematic comparison empirically of the performances of the MAC a n d F C algorithms on large and hard CSPs. In particular, we compare their performance with regard to the size, constraint density and constraint t i g h tness of the problems. Though there is a trend that MAC e v entually outperforms FC on hard problems as we increase the problem size, we found that the superiority o f M A C o ver FC w ould not be revealed on the hard problems with low constraint t i g h tness and high constraint density u n til the size of these problems is quite large. We also devised a new FC algorithm | FC4, which s h o ws good performance on the hard problems with low constraint tightness and high constraint density. iv I w ould also like to thank Jean-Charles Regin of ILOG for providing his programs, and his assistance in my understanding his algorithms.
Preprocessing versus Search Processing for Constraint Satisfaction Problems
2016
A perennial problem in hybrid backtrack CSP search is how much local consistency processing should be done to achieve the best efficiency. This can be divided into two separate questions: (1) how much work should be done before the actual search begins, i.e. during preprocessing?, and (2) how much of the same processing should be interleaved with search? At present there are two leading approaches to establishing stronger consistencies than the basic arc consistency maintenance that is done in most solvers. On the one hand there are various kinds singleton arc consistency that can be used; on the other there are several variants of restricted path consistency. To date these have not been compared directly. The present work attempts to do this for a variety of problems, and in so doing, it also provides an empirical evaluation of the preprocessing versus search processing issue. Comparisons are made using the domain/degree and domain/weighted degree variable ordering heuristics. In g...
International Journal of Advanced Research in Artificial Intelligence, 2012
Many researchers in Artificial Intelligence seek for new algorithms to reduce the amount of memory/ time consumed for general searches in Constraint Satisfaction Problems. These improvements are accomplished by the use of heuristics which either prune useless tree search branches or even indicate the path to reach the (optimal) solution faster than the blind version of the search. Many heuristics were proposed in the literature, like the Least Constraining Value (LCV). In this paper we propose a new pre-processing search heuristic to reduce the amount of backtracking calls, namely the Least Suggested Value First: a solution whenever the LCV solely cannot measure how much a value is constrained. In this paper, we present a pedagogical example, as well as the preliminary results.
New look-ahead schemes for constraint satisfaction
2004
This paper presents new look-ahead schemes for backtracking search when solving constraint satisfaction problems. The look-ahead schemes compute a heuristic for value ordering and domain pruning, which influences variable orderings at each node in the search space. As a basis for a heuristic, we investigate two tasks, both harder than the CSP task. The first is finding the solution with min-number of conflicts. The second is counting solutions. Clearly each of these tasks also finds a solution to the CSP problem, if one exists, or decides that the problem is inconsistent. Our plan is to use approximations of these more complex tasks as heuristics for guiding search for a solution of a CSP task. In particular, we investigate two recent partitionbased strategies that approximate variable elimination algorithms, Mini-Bucket-Tree Elimination and Iterative Join-Graph Propagation (ijgp). The latter belong to the class of belief propagation algorithm that attracted substantial interest due to their surprising success for probabilistic inference. Our preliminary empirical evaluation is very encouraging, demonstrating that the countingbased heuristic approximated by by IJGP yields a very focused search even for hard problems.