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Statistical mechanics of combinatorial search
 In Proc. of the Workshop on Physics and Computation (PhysComp94
, 1994
"... The statistical mechanics of combinatorial search problems is described using the example of the wellknown NPcomplete graph coloring problem. We focus on a recently identified phase transition from under to overconstrained problems, near which are concentrated many hard to solve search problems. ..."
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Cited by 19 (5 self)
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The statistical mechanics of combinatorial search problems is described using the example of the wellknown NPcomplete graph coloring problem. We focus on a recently identified phase transition from under to overconstrained problems, near which are concentrated many hard to solve search problems. Thus, a readily computed measure of problem structure predicts the difficulty of solving the problem, on average. However, this prediction is associated with a large variance and depends on the somewhat arbitrary choice of the problem ensemble. Thus these results are of limited direct use for individual instances. To help address this limitation, additional parameters, describing problem structure as well as heuristic effectiveness, are introduced. This also highlights the distinction between the statistical mechanics of combinatorial search problems, with their exponentially large search spaces, and physical systems, whose interactions are often governed by a simple euclidean metric. Chapter 1
An attempt to map the performance of a range of algorithm and heuristic combinations
 IN HYBRID PROBLEMS, HYBRID SOLUTIONS
, 1995
"... Constraint satisfaction is the core of many AI and real life problems and much research has been done in this field in recent years. Work has been done in the past on comparing the performance of different algorithms and heuristics. Much of such work has focused on finding "the best" algor ..."
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Cited by 18 (1 self)
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Constraint satisfaction is the core of many AI and real life problems and much research has been done in this field in recent years. Work has been done in the past on comparing the performance of different algorithms and heuristics. Much of such work has focused on finding "the best" algorithm and heuristic combination for all problems. The objective of this paper is to prove that there is no universally best algorithm and heuristic for all problems different problems can be solved most efficiently by different algorithm and heuristic combinations. The implication of this is important because it means that instead of trying to find "the best " algorithms and heuristics, future research should try to identify the application domain of each algorithm and heuristic (i.e. when they are most effective). Furthermore our results point to future research which focuses on how to retrieve the most efficient algorithm for a given problem. The results in this paper provide a first step towards achieving such goals.
Improving Graphplan's search with EBL & DDB techniques
 In Proc. IJCAI99
, 1999
"... I highlight some inefficiencies of Graphplan’s backward search algorithm, and describe how these can be eliminated by adding explanationbased learning and dependencydirected backtracking capabilities to Graphplan. I will then demonstrate the effectiveness of these augmentations by describing resul ..."
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Cited by 17 (5 self)
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I highlight some inefficiencies of Graphplan’s backward search algorithm, and describe how these can be eliminated by adding explanationbased learning and dependencydirected backtracking capabilities to Graphplan. I will then demonstrate the effectiveness of these augmentations by describing results of empirical studies that show dramatic improvements in runtime ( 100x speedups) as well as solvabilityhorizons on benchmark problems across seven different domains. 1
Extending forward checking
 in Proceedings of CP’00
, 2000
"... Abstract. Among backtracking based algorithms for constraint satisfaction problems (CSPs), algorithms employing constraint propagation, like forward checking (FC) and MAC, have had the most practical impact. These algorithms use constraint propagation during search to prune inconsistent values from ..."
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Cited by 16 (4 self)
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Abstract. Among backtracking based algorithms for constraint satisfaction problems (CSPs), algorithms employing constraint propagation, like forward checking (FC) and MAC, have had the most practical impact. These algorithms use constraint propagation during search to prune inconsistent values from the domains of the uninstantiated variables. In this paper we present a general approach to extending constraint propagating algorithms, especially forward checking. In particular, we provide a simple yet flexible mechanism for pruning domain values, and show that with this in place it becomes easy to utilize new mechanisms for detecting inconsistent values during search. This leads to a powerful and uniform technique for designing new CSP algorithms: one simply need design new methods for detecting inconsistent values and then interface them with the domain pruning mechanism. Furthermore, we also show that algorithms following this design can proved to be correct in a simple and uniform way. To demonstrate the utility of these ideas five “new ” CSP algorithms are presented. 1
Procedural Reasoning in Constraint Satisfaction
, 1996
"... For many constraint satisfaction problems, there are well known, fast algorithms and functions that solve parts of the problem. Using these methods directly to solve the subproblems significantly speeds up the solving process. Unfortunately, doing this has usually required the solver to be changed, ..."
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Cited by 15 (5 self)
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For many constraint satisfaction problems, there are well known, fast algorithms and functions that solve parts of the problem. Using these methods directly to solve the subproblems significantly speeds up the solving process. Unfortunately, doing this has usually required the solver to be changed, or the correctness criteria to be reexamined. We describe a general mechanism to use procedures with almost any search engine, such that it is easy to add any procedures without changing the engine. Furthermore, the framework is formally defined, which allows us to prove conditions that are sufficient to guarantee systematicity and completeness for search engines using procedures. 1 Introduction For many constraint satisfaction problems there are simple functional relations (e.g. arithmetic equations) and simple subproblems (e.g. linear equations with unknowns) that can be solved quickly, using simple algorithms. Needless to say, taking advantage of such algorithms can significantly decrea...
How Not To Do It
, 1997
"... We give some dos and don'ts for those analysing algorithms experimentally. We illustrate these with many examples from our own research on the study of algorithms for NPcomplete problems such as satisfiability and constraint satisfaction. Where we have not followed these maxims, we have suffer ..."
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Cited by 14 (1 self)
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We give some dos and don'ts for those analysing algorithms experimentally. We illustrate these with many examples from our own research on the study of algorithms for NPcomplete problems such as satisfiability and constraint satisfaction. Where we have not followed these maxims, we have suffered as a result. 1 Introduction The empirical study of algorithms is a relatively immature field with many technical and scientific problems. We support the calls of McGeoch (1986,1996), Hooker (1994), and others for a more scientific approach to the empirical study of algorithms. Our contribution in this paper is colloquial. We admit to a large number of mistakes in conducting our research. While painful, we hope that this will encourage others to avoid these mistakes, and thereby to develop practices which represent good science. Much of our research has been on the experimental analysis of algorithms and phase transitions in NPcomplete problems, most commonly in satisfiability or constraint s...
Forward Checking with Backmarking
, 1993
"... The forward checking routine (FC) of Haralick and Elliott attempts to encourage early failures within the search tree of constraint satisfaction problems, leading to a reduction in nodes visited, which tends to result in reduced search effort. In contrast, Gaschnig's backmarking routine (BM) ..."
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Cited by 13 (0 self)
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The forward checking routine (FC) of Haralick and Elliott attempts to encourage early failures within the search tree of constraint satisfaction problems, leading to a reduction in nodes visited, which tends to result in reduced search effort. In contrast, Gaschnig's backmarking routine (BM) attempts to avoid performing redundant consistency checks. These two algorithms are combined to give us FCBM, an algorithm that attempts to minimise the number of nodes visited, while avoiding redundant consistency checks. This algorithm is further enhanced such that it incorporates conflictdirected backjumping (CBJ) to give us FCBMCBJ. A series of experiments are then carried out on really hard problems in an attempt to position these new algorithms with respect to the known algorithms.
On the Relations between Intelligent Backtracking and Failuredriven Explanation Based Learning in Constraint Satisfaction and Planning
, 1998
"... The ideas of intelligent backtracking (IB) and explanationbased learning (EBL) have developed independently in the constraint satisfaction, planning, machine learning and problem solving communities. The variety of approaches developed for IB and EBL in the various communities have hitherto been i ..."
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Cited by 11 (6 self)
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The ideas of intelligent backtracking (IB) and explanationbased learning (EBL) have developed independently in the constraint satisfaction, planning, machine learning and problem solving communities. The variety of approaches developed for IB and EBL in the various communities have hitherto been incomparable. In this paper, I formalize and unify these ideas under the taskindependent framework of refinement search, which can model the search strategies used in both planning and constraint satisfaction problems (CSPs). I show that both IB and EBL depend upon the common theory of explanation analysiswhich involves explaining search failures, and regressing them to higher levels of the search tree. My comprehensive analysis shows that most of the differences between the CSP and planning approaches to EBL and IB revolve around different solutions to: (a) how the failure explanations are computed; (b) how they are contextualized (contextualization involves deciding whether or not to keep the flaw description and the description of the violated problem constraints); and (c) how the storage of explanations is managed. The differences themselves can be understood in terms of the differences between planning and CSP problems as instantiations of refinement search. This unified understanding is expected to support a greater crossfertilization of ideas among CSP, planning and EBL communities.
A Framework for Integrating Artificial Neural Networks and Logic Programming
 INTERNATIONAL JOURNAL ON ARTIFICIAL INTELLIGENCE TOOLS
, 1995
"... Many reallife problems belong to the class of constraint satisfaction problems (CSP's), which are NPcomplete, and some NPhard, in general. When the problem size grows, it becomes difficult to program solutions and to execute the solution in a timely manner. In this paper, we present a gen ..."
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Cited by 11 (8 self)
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Many reallife problems belong to the class of constraint satisfaction problems (CSP's), which are NPcomplete, and some NPhard, in general. When the problem size grows, it becomes difficult to program solutions and to execute the solution in a timely manner. In this paper, we present a general framework for integrating artificial neural networks and logic programming to provide an efficient and yet easytoprogram environment for solving CSP's. To realize this framework, we propose a novel constraint logic programming language PROCLANN. Operationally, PROCLANN uses the standard goal reduction strategy as frontend to generate constraints and an efficient backend constraintsolver based on artificial neural networks. PROCLANN retains the simple and elegant declarative semantics of constraint logic programming. Its operational semantics is probabilistic in nature. We show that PROCLANN is sound and weakly complete. A novelty of PROCLANN is that while it is a committedchoice l...
Backtracking Search Algorithms
, 2006
"... There are three main algorithmic techniques for solving constraint satisfaction problems: backtracking search, local search, and dynamic programming. In this chapter, I survey backtracking search algorithms. Algorithms based on dynamic programming [15]— sometimes referred to in the literature as var ..."
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Cited by 10 (2 self)
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There are three main algorithmic techniques for solving constraint satisfaction problems: backtracking search, local search, and dynamic programming. In this chapter, I survey backtracking search algorithms. Algorithms based on dynamic programming [15]— sometimes referred to in the literature as variable elimination, synthesis, or inference algorithms—are the topic of Chapter 7. Local or stochastic search algorithms are the topic of Chapter 5. An algorithm for solving a constraint satisfaction problem (CSP) can be either complete or incomplete. Complete, or systematic algorithms, come with a guarantee that a solution will be found if one exists, and can be used to show that a CSP does not have a solution and to find a provably optimal solution. Backtracking search algorithms and dynamic programming algorithms are, in general, examples of complete algorithms. Incomplete, or nonsystematic algorithms, cannot be used to show a CSP does not have a solution or to find a provably optimal solution. However, such algorithms are often effective at finding a solution if one exists and can be used to find an approximation to an optimal solution. Local or stochastic search algorithms are examples of incomplete algorithms. Of the two