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Search in a Small World
, 1998
"... In a graph with a "small world" topology, nodes are highly clustered yet the path length between them is small. Such a topology can make search problems very difficulty since local decisions quickly propagate globally. We show that graphs associated with many different search problem ..."
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Cited by 119 (13 self)
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In a graph with a "small world" topology, nodes are highly clustered yet the path length between them is small. Such a topology can make search problems very difficulty since local decisions quickly propagate globally. We show that graphs associated with many different search problems have a small world topology, and that the cost of solving search problems with such a topology can have a heavytailed distribution.
Random constraint satisfaction: Flaws and structure
 Constraints
, 2001
"... 4, and Toby Walsh 5 ..."
MAC and Combined Heuristics: Two Reasons to Forsake FC (and CBJ?) on Hard Problems
 In Proceedings of the Second International Conference on Principles and Practice of Constraint Programming
, 1996
"... . In the last twenty years, many algorithms and heuristics were developed to find solutions in constraint networks. Their number increased to such an extent that it quickly became necessary to compare their performances in order to propose a small number of "good" methods. These comparison ..."
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Cited by 49 (3 self)
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. In the last twenty years, many algorithms and heuristics were developed to find solutions in constraint networks. Their number increased to such an extent that it quickly became necessary to compare their performances in order to propose a small number of "good" methods. These comparisons often led us to consider FC or FCCBJ associated with a "minimum domain" variable ordering heuristic as the best techniques to solve a wide variety of constraint networks. In this paper, we first try to convince once and for all the CSP community that MAC is not only more efficient than FC to solve large practical problems, but it is also really more efficient than FC on hard and large random problems. Afterwards, we introduce an original and efficient way to combine variable ordering heuristics. Finally, we conjecture that when a good variable ordering heuristic is used, CBJ becomes an expensive gadget which almost always slows down the search, even if it saves a few constraint checks. 1 Introducti...
Adaptive Constraint Satisfaction: The Quickest First Principle
 EUROPEAN CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 1996
"... The choice of a particular algorithm for solving a given class of constraint satisfaction problems is often confused by exceptional behaviour of algorithms. One method of reducing the impact of this exceptional behaviour is to adopt an adaptive philosophy to constraint satisfaction problem solving. ..."
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Cited by 36 (3 self)
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The choice of a particular algorithm for solving a given class of constraint satisfaction problems is often confused by exceptional behaviour of algorithms. One method of reducing the impact of this exceptional behaviour is to adopt an adaptive philosophy to constraint satisfaction problem solving. In this report we describe one such adaptive algorithm, based on the principle of chaining. It is designed to avoid the phenomenon of exceptionally hard problem instances. Our algorithm shows how the speed of more naïve algorithms can be utilised safe in the knowledge that the exceptional behaviour can be bounded. Our work clearly demonstrates the potential benefits of the adaptive approach and opens a new front of research for the constraint satisfaction community.
The Phase Transition Behaviour of Maintaining Arc Consistency
 In Proceedings of ECAI96
, 1995
"... In this paper, we study two recently presented algorithms employing a "full lookahead" strategy: MAC (Maintaining Arc Consistency); and the hybrid MACCBJ, which combines conflictdirected backjumping capability with MAC. We observe their behaviour with respect to the phase transition pro ..."
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Cited by 26 (7 self)
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In this paper, we study two recently presented algorithms employing a "full lookahead" strategy: MAC (Maintaining Arc Consistency); and the hybrid MACCBJ, which combines conflictdirected backjumping capability with MAC. We observe their behaviour with respect to the phase transition properties of randomlygenerated binary constraint satisfaction problems, and investigate the benefits of maintaining a higher level of consistency during search by comparing MAC and MACCBJ with the FC and FCCBJ algorithms, which maintain only node consistency. The phase transition behaviour that has been observed for many classes of problem as a control parameter is varied has prompted a flurry of research activity in recent years. Studies of these transitions, from regions where most problems are easy and soluble to regions where most are easy but insoluble, have raised a number of important issues such as the phenomenon of exceptionally hard problems ("ehps") in the easysoluble region, and the grow...
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 18 (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...
Randomness and Structure
"... This chapter covers research in constraint programming (CP) and related areas involving random problems. Such research has played a significant role in the development of more efficient and effective algorithms, as well as in understanding the source of hardness in solving combinatorially challengin ..."
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Cited by 9 (3 self)
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This chapter covers research in constraint programming (CP) and related areas involving random problems. Such research has played a significant role in the development of more efficient and effective algorithms, as well as in understanding the source of hardness in solving combinatorially challenging problems. Random problems have proved useful in a number of different ways. Firstly, they provide a relatively “unbiased ” sample for benchmarking algorithms. In the early days of CP, many algorithms were compared using only a limited sample of problem instances. In some cases, this may have lead to premature conclusions. Random problems, by comparison, permit algorithms to be tested on statistically significant samples of hard problems. However, as we outline in the rest of this chapter, there remain pitfalls waiting the unwary in their use. For example, random problems may not contain structures found in many real world problems, and these structures can make problems much easier or much harder to solve. As a second example, the process of generating random problems may itself be “flawed”, giving problem instances which are not, at least asymptotically, combinatorially hard. Random problems have also provided insight into problem hardness. For example, the influential paper by Cheeseman, Kanefsky and Taylor [12] highlighted the computational difficulty of problems which are on the “knifeedge ” between satisfiability and unsatisfiability [84]. There is even hope within certain quarters that random problems may be one of the links in resolving the P=NP question. Finally, insight into problem hardness provided by random problems has helped inform the design of better algorithms and heuristics. For example, the design of a number of branching heuristics for the Davis Logemann Loveland satisfiability (DPLL) procedure has been heavily influenced by the hardness of random problems. As a second example, the rapid randomization and restart (RRR) strategy [45, 44] was motivated by the discovery of heavytailed runtime distributions in backtracking style search procedures on random quasigroup completion problems.
Modelling more realistic sat problems
 In Australian Joint Conference on Artificial Intelligence
, 2002
"... Abstract. The satisfiability problem is widely used in research on combinatorial search and for industrial applications such as verification and planning. Real world search problem benchmarks are not plentiful, yet understanding search algorithm behaviour in the real world domain is highly important ..."
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Cited by 5 (0 self)
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Abstract. The satisfiability problem is widely used in research on combinatorial search and for industrial applications such as verification and planning. Real world search problem benchmarks are not plentiful, yet understanding search algorithm behaviour in the real world domain is highly important. This work justifies and investigates a randomised satisfiability problem model with modular properties akin to those observed in real world search problem domains. The proposed problem model provides a reliable benchmark which highlights pitfalls and advantages with various satisfiability search algorithms. 1
Scotland
"... We introduce a mechanism called “morphing ” for introducing structure or randomness into a wide variety of problems. We illustrate the usefulness of morphing by performing several different experimental studies. These studies identify the impact of a “smallworld ” topology on the cost of coloring g ..."
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We introduce a mechanism called “morphing ” for introducing structure or randomness into a wide variety of problems. We illustrate the usefulness of morphing by performing several different experimental studies. These studies identify the impact of a “smallworld ” topology on the cost of coloring graphs, of asymmetry on the cost of finding the optimal TSP tour, and of the dimensionality of space on the cost of finding the optimal TSP tour. We predict that morphing will find many other uses.
2004 Kluwer Academic Publishers. Manufactured in The Netherlands. Graph Coloring for Air Traffic Flow Management
"... Abstract. The aim of Air Traffic Flow Management (ATFM) is to enhance the capacity of the airspace while satisfying Air Traffic Control constraints and airlines requests to optimize their operating costs. This paper presents a design of a new route network that tries to optimize these criteria. The ..."
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Abstract. The aim of Air Traffic Flow Management (ATFM) is to enhance the capacity of the airspace while satisfying Air Traffic Control constraints and airlines requests to optimize their operating costs. This paper presents a design of a new route network that tries to optimize these criteria. The basic idea is to consider direct routes only and vertically separate intersecting ones by allocating distinct flight levels, thus leading to a graph coloring problem. This problem is solved using constraint programming after having found large cliques with a greedy algorithm. These cliques are used to post global constraints and guide the search strategy. With an implementation using FaCiLe, our Functional Constraint Library, optimality is achieved for all instances except the largest one, while the corresponding number of flight levels could fit in the current airspace structure. This graph coloring technique has also been tested on various benchmarks, featuring good results on reallife instances, which systematically appear to contain large cliques.