We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Constraint programming is a powerful paradigm for solving combinatorial search problems that draws on a wide range of techniques from artificial intelligence, computer science, databases, programming languages, and operations research. Constraint programming is currently applied with success to many domains, such as scheduling, planning, vehicle routing, configuration, networks, and bioinformatics.

The aim of this handbook is to capture the full breadth and depth of the constraint programming field and to be encyclopedic in its scope and coverage. While there are several excellent books on constraint programming, such books necessarily focus on the main notions and techniques and cannot cover also extensions, applications, and languages. The handbook gives a reasonably complete coverage of all these lines of work, based on constraint programming, so that a reader can have a rather precise idea of the whole field and its potential. Of course each line of work is dealt with in a survey-like style, where some details may be neglected in favor of coverage. However, the extensive bibliography of each chapter will help the interested readers to find suitable sources for the missing details. Each chapter of the handbook is intended to be a self-contained survey of a topic, and is written by one or more authors who are leading researchers in the area.

The intended audience of the handbook is researchers, graduate students, higher-year undergraduates and practitioners who wish to learn about the state-of-the-art in constraint programming. No prior knowledge about the field is necessary to be able to read the chapters and gather useful knowledge. Researchers from other fields should find in this handbook an effective way to learn about constraint programming and to possibly use some of the constraint programming concepts and techniques in their work, thus providing a means for a fruitful cross-fertilization among different research areas.

The handbook is organized in two parts. The first part covers the basic foundations of constraint programming, including the history, the notion of constraint propagation, basic search methods, global constraints, tractability and computational complexity, and important issues in modeling a problem as a constraint problem. The second part covers constraint languages and solver, several useful extensions to the basic framework (such as interval constraints, structured domains, and distributed CSPs), and successful application areas for constraint programming.

- Covers the whole field of constraint programming
- Survey-style chapters
- Five chapters on applications

Table of Contents

Foreword (Ugo Montanari) 
Part I : Foundations
Chapter 1. Introduction (Francesca Rossi, Peter van Beek, Toby Walsh) 
Chapter 2. Constraint Satisfaction: An Emerging Paradigm (Eugene C. Freuder, Alan K. Mackworth) 
Chapter 3. Constraint Propagation (Christian Bessiere) 
Chapter 4. Backtracking Search Algorithms (Peter van Beek) 
Chapter 5. Local Search Methods (Holger H. Hoos, Edward Tsang) 
Chapter 6. Global Constraints (Willem-Jan van Hoeve, Irit Katriel)
Chapter 7. Tractable Structures for CSPs (Rina Dechter)
Chapter 8. The Complexity of Constraint Languages
(David Cohen, Peter Jeavons) 
Chapter 9. Soft Constraints (Pedro Meseguer, Francesca Rossi, Thomas Schiex) 
Chapter 10. Symmetry in Constraint Programming
(Ian P. Gent, Karen E. Petrie, Jean-Francois Puget)
Chapter 11. Modelling (Barbara M. Smith) 
Part II : Extensions, Languages, and Applications

Chapter 12. Constraint Logic Programming (Kim Marriott, Peter J. Stuckey, Mark Wallace) 
Chapter 13. Constraints in Procedural and Concurrent Languages (Thom Fruehwirth, Laurent Michel, Christian Schulte)
Chapter 14. Finite Domain Constraint Programming Systems (Christian Schulte, Mats Carlsson) 
Chapter 15. Operations Research Methods in Constraint Programming (John Hooker) 
Chapter 16. Continuous and Interval Constraints(Frederic Benhamou, Laurent Granvilliers) 
Chapter 17. Constraints over Structured Domains
(Carmen Gervet) 
Chapter 18. Randomness and Structure (Carla Gomes, Toby Walsh)
Chapter 19. Temporal CSPs (Manolis Koubarakis)
Chapter 20. Distributed Constraint Programming
(Boi Faltings) 
Chapter 21. Uncertainty and Change (Kenneth N. Brown, Ian Miguel)
Chapter 22. Constraint-Based Scheduling and Planning
(Philippe Baptiste, Philippe Laborie, Claude Le Pape, Wim Nuijten)
Chapter 23. Vehicle Routing (Philip Kilby, Paul Shaw) 
Chapter 24. Configuration (Ulrich Junker)
Chapter 25. Constraint Applications in Networks
(Helmut Simonis)
Chapter 26. Bioinformatics and Constraints (Rolf Backofen, David Gilbert)

/pdf/handbook-of-constraint-programming-53srutguo2.pdf

Handbook of Constraint Programming

Associate DIETRICH BELITZ, University of Oregon Editors: Condensed Matter Physics (Theoretical) J. IGNACIO CIRAC, Max-Planck-Institut für Quantenoptik Quantum Information RAYMOND E. GOLDSTEIN, University of Cambridge Biological Physics ARTHUR F. HEBARD, University of Florida Condensed Matter Physics (Experimental) RANDALL D. KAMIEN, University of Pennsylvania Soft Condensed Matter DANIEL KLEPPNER, Massachusetts Institute of Technology Atomic, Molecular, and Optical Physics (Experimental) PAUL G. LANGACKER, Institute for Advanced Study, Princeton University Particle Physics (Theoretical) VERA LÜTH, Stanford University Particle Physics (Experimental) DAVID D. MEYERHOFER, University of Rochester Physics of Plasmas and Matter at High-Energy Density WITOLD NAZAREWICZ, University of Tennessee, Oak Ridge National Laboratory Nuclear Physics JOHN H. SCHWARZ, California Institute of Technology Mathematical Physics FRIEDRICH-KARL THIELEMANN, Universität Basel Astrophysics Senior Assistant Editor: DEBBIE BRODBAR, APS Editorial Office American Physical Society

Reviews of Modern Physics

We present in this paper a new, complete method for distributed constraint optimization, based on dynamic programming. It is a utility propagation method, inspired by the sum-product algorithm, which is correct only for tree-shaped constraint networks. In this paper, we show how to extend that algorithm to arbitrary topologies using a pseudotree arrangement of the problem graph. Our algorithm requires a linear number of messages, whose maximal size depends on the induced width along the particular pseudotree chosen.

We compare our algorithm with backtracking algorithms, and present experimental results. For some problem types we report orders of magnitude fewer messages, and the ability to deal with arbitrarily large problems. Our algorithm is formulated for optimization problems, but can be easily applied to satisfaction problems as well.

/pdf/a-scalable-method-for-multiagent-constraint-optimization-mm6cwwbmbp.pdf

A scalable method for multiagent constraint optimization

In the multi agent path finding problem (MAPF) paths should be found for several agents, each with a different start and goal position such that agents do not collide. Previous optimal solvers applied global A*-based searches. We present a new search algorithm called Conflict Based Search (CBS). CBS is a two-level algorithm. At the high level, a search is performed on a tree based on conflicts between agents. At the low level, a search is performed only for a single agent at a time. In many cases this reformulation enables CBS to examine fewer states than A* while still maintaining optimality. We analyze CBS and show its benefits and drawbacks. Experimental results on various problems shows a speedup of up to a full order of magnitude over previous approaches.

Conflict-based search for optimal multi-agent path finding

A new search algorithm for solving distributed constraint optimization problems (DisCOPs) is presented. Agents assign variables sequentially and compute bounds on partial assignments asynchronously. The asynchronous bounds computation is based on the propagation of partial assignments. The asynchronous forward-bounding algorithm (AFB) is a distributed optimization search algorithm that keeps one consistent partial assignment at all times. The algorithm is described in detail and its correctness proven. Experimental evaluation shows that AFB outperforms synchronous branch and bound by many orders of magnitude, and produces a phase transition as the tightness of the problem increases. This is an analogous effect to the phase transition that has been observed when local consistency maintenance is applied to MaxCSPs. The AFB algorithm is further enhanced by the addition of a backjumping mechanism, resulting in the AFB-BJ algorithm. Distributed backjumping is based on accumulated information on bounds of all values and on processing concurrently a queue of candidate goals for the next move back. The AFB-BJ algorithm is compared experimentally to other DisCOP algorithms (ADOPT, DPOP, OptAPO) and is shown to be a very efficient algorithm for DisCOPs.

/pdf/asynchronous-forward-bounding-for-distributed-cops-ppyzb7u9aj.pdf

Asynchronous forward bounding for distributed COPs

http://www.bgu.ac.il/~zivanr/files/ALS_AIJ.pdf

Explorative anytime local search for distributed constraint optimization

Coordinating a mobile sensor team (MST) to cover targets is a challenging problem in many multiagent applications. Such applications are inherently dynamic due to changes in the environment, technology failures, and incomplete knowledge of the agents. Agents must adaptively respond by changing their locations to continually optimize the coverage of targets. We propose distributed constraint optimization problems (DCOP)_MST, a new model for representing MST problems that is based on DCOP. In DCOP_MST, agents maintain variables for their physical positions, while each target is represented by a constraint that reflects the quality of coverage of that target. In contrast to conventional, static DCOPs, DCOP_MST not only permits dynamism but exploits it by restricting variable domains to nearby locations; consequently, variable domains and constraints change as the agents move through the environment. DCOP_MST confers three major advantages. It directly represents the multiple forms of dynamism inherent in MSTs. It also provides a compact representation that can be solved efficiently with local search algorithms, with information and communication locality based on physical locality as typically occurs in MST applications. Finally, DCOP_MST facilitates organization of the team into multiple sub-teams that can specialize in different roles and coordinate their activity through dynamic events. We demonstrate how a search-and-detection team responsible for finding new targets and a surveillance sub-team tasked with coverage of known targets can effectively work together to improve performance while using the DCOP_MST framework to coordinate. We propose different algorithms to meet the specific needs of each sub-team and several methods for cooperation between sub-teams. For the search-and-detection team, we develop an algorithm based on the DSA that forces intensive exploration for new targets. For the surveillance sub-team, we adapt several incomplete DCOP algorithms, including MGM, DSA, DBA, and Max-sum, which requires us to develop an efficient method for agents to find the value assignment in their local environment that is optimal in minimizing the maximum unmet coverage requirement over all targets. The disadvantage of dynamic domains based on physical locality is that adaptations of standard local search algorithms tend to become trapped in local optima where targets beyond the immediate range of the agents go uncovered. To address this shortcoming we develop exploration methods to be used with the local search algorithms. Our algorithms are extensively evaluated in a simulation environment. We use a reputation model to determine the individual credibility of agents and consider both additive and submodular joint credibility functions for determining coverage of targets by multiple agents. The performance is measured on two objectives: minimizing the maximum remaining coverage requirement, and minimizing the sum of remaining coverage requirements. Our results show that DSA and MGM with the exploration heuristics outperform the other incomplete algorithms across a wide range of settings. Furthermore, organizing the team into two sub-teams leads to significant gains in performance, and performance continues to improve with greater cooperation between the sub-teams.

Distributed constraint optimization for teams of mobile sensing agents

Distributed constraint satisfaction problems (DisCSPs) are composed of agents, each holding its own variables, that are connected by constraints to variables of other agents. Due to the distributed nature of the problem, message delay can have unexpected effects on the behavior of distributed search algorithms on DisCSPs. This has been recently shown in experimental studies of asynchronous backtracking algorithms (Bejar et al., Artif. Intell., 161:117---148, 2005; Silaghi and Faltings, Artif. Intell., 161:25---54, 2005). To evaluate the impact of message delay on the run of DisCSP search algorithms, a model for distributed performance measures is presented. The model counts the number of non concurrent constraints checks, to arrive at a solution, as a non concurrent measure of distributed computation. A simpler version measures distributed computation cost by the non-concurrent number of steps of computation. An algorithm for computing these distributed measures of computational effort is described. The realization of the model for measuring performance of distributed search algorithms is a simulator which includes the cost of message delays. Two families of distributed search algorithms on DisCSPs are investigated. Algorithms that run a single search process, and multiple search processes algorithms. The two families of algorithms are described and associated with existing algorithms. The performance of three representative algorithms of these two families is measured on randomly generated instances of DisCSPs with delayed messages. The delay of messages is found to have a strong negative effect on single search process algorithms, whether synchronous or asynchronous. Multi search process algorithms, on the other hand, are affected very lightly by message delay.

http://fohs.bgu.ac.il/research/upload/21175/Msg_Delay_Jou_Rev2.pdf

Message delay and DisCSP search algorithms

A new search algorithm for solving distributed constraint satisfaction problems (DisCSPs) is presented. Agents assign variables sequentially, but perform forward checking asynchronously. The asynchronous forward-checking algorithm (AFC) is a distributed search algorithm that keeps one consistent partial assignment at all times. Forward checking is performed by sending copies of the partial assignment to all unassigned agents concurrently. The algorithm is described in detail and its correctness proven. The sequential assignment method of AFC leads naturally to dynamic ordering of agents during search. Several ordering heuristics are presented. The three best heuristics are evaluated and shown to improve the performance of AFC with static order by a large factor. An experimental comparison of AFC to asynchronous backtracking (ABT) on randomly generated DisCSPs is also presented. AFC with ordering heuristics outperforms ABT by a large factor on the harder instances of random DisCSPs. These results hold for two measures of performance: number of non-concurrent constraints checks and number of messages sent.

/pdf/asynchronous-forward-checking-for-discsps-1lkg4xijps.pdf

Roie Zivan

Papers

Asynchronous forward bounding for distributed COPs

Explorative anytime local search for distributed constraint optimization

Distributed constraint optimization for teams of mobile sensing agents

Message delay and DisCSP search algorithms

Asynchronous Forward-checking for DisCSPs