Marius C. Silaghi (Florida Institute of Technology, USA) and Makoto Yokoo (Kyushu University, Japan)

DOI: 10.4018/978-1-59904-849-9.ch077

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TopDistributed constraint reasoning is concerned with modeling and solving naturally distributed problems. It has application to the coordination and negotiation between semi-cooperative agents, namely agents that want to achieve a common goal but would not give up private information over secret constraints. When compared to centralized constraint satisfaction (CSP) and constraint optimization (COP), one of the most expensive operations is communication. Other differences stem from new coherence and privacy needs. We review approaches based on asynchronous backtracking and depth-first search spanning trees.

Distributed constraint reasoning started as an outgrowth of research in constraints and multi-agent systems. Take the sensors network problem in Figure 1, defined by a set of geographically distributed sensors that have to track a set of mobile nodes. Each sensor can watch only a subset of its neighborhood at a given time. Three sensors need to simultaneously focus on the same mobile node in order to locate it. Approaches modeling and solving this problem with distributed constraint reasoning are described in (Bejar, Domshlak, Fernandez, Gomes, Krishnamachari, Selman, &Valls, 2005).

There are two large classes of distributed constraint problems. The first class is described by a set of *Boolean relations* (aka *constraints*) on possible assignments of variables, where the relations are distributed among agents. They are called distributed constraint satisfaction problems (DisCSPs). The challenge is to find assignments of variables to values such that all these relations are satisfied. However, the reasoning process has to be performed by collaboration among the agents. There exist several solutions to a problem, and ties have to be broken by some priority scheme. Such priorities may be imposed from the problem description where some agents, such as government agencies, are more important than others. In other problems it is important to ensure that different solutions or participants have equal chances, and this property is called *uniformity*. When no solution exists, one may still want to find an assignment of the variables that conflict as few constraints as possible. The second class of problems refers to numerical optimization described by a set of functions (*weighted constraints*) defined on assignments of variables and returning positive numerical values. The goal is to find assignments that minimize the objective function defined by the sum of these functions. The problems obtained in this way are called distributed constraint optimization problems (DisCOPs). Some problems require a fair distribution of the amount of dissatisfaction among agents, minimizing the dissatisfaction of the most unsatisfied agent.

There are also two different ways of distributing a problem. The first way consists of distributing the data associated with it. It is defined in terms of which agents know which constraints. It can be shown that any such problem can be translated into problems where all non-shared constraints are *unary* (constraints involving only one variable), also called *domain constraints*. Here one can assume that there exists a single unary constraint for each variable. It is due to the fact that any second unary constraint can be reformulated on a new variable, required to be equal to the original variable. The agent holding the unique domain constraint of a variable is called the *owner of that variable*. Due to the availability of this transformation many solutions focus on the case where only the unary constraints are not shared by everybody (also said to be private to the agents that know them). Another common simplification consists in assuming that each agent has a single unary constraint (i.e., a single variable). This simplification does not reduce the generality of the addressable problems since an agent can participate in a computation under several names, e.g., one instance for each unary constraint of the original agent. Such false identities for an agent are called pseudo-agents (Modi, Shen, Tambe, & Yokoo, 2005), or abstract agents (Silaghi & Faltings, 2005).

Nogood: A logic statement about combinations of assignments that are penalized due to some constraints.

Agent: A participant in a distributed computation, having its own constraints.

DisCSP: Distributed Constraint Satisfaction Problem framework (also DCSP).

Constraint: A relation between variables specifying a subset of their Cartesian product that is not permitted. Optionally it can also specify numeric penalties for those tuples.

Optimality: The quality of an algorithm of returning only solutions that are at least as good as any other solution.

DisCOP: Distributed Constraint Optimization Problem framework (also DCOP).

Quiescence: The state of being inactive. The system will not change without an external stimulus.

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Rule Engines and Agent-Based Systems
(pages 1404-1410)

Agostino Poggi, Michele Tomaiuolo

$37.50

Chapter 207

Sequence Processing with Recurrent Neural Networks
(pages 1411-1417)

Chun-Cheng Peng, George D. Magoulas

$37.50

Chapter 208

Shortening Automated Negotiation Threads via Neural Nets
(pages 1418-1425)

Ioanna Roussaki, Ioannis Papaioannou, Miltiades Anagnostou

$37.50

Chapter 209

Signed Formulae as a New Update Process
(pages 1426-1432)

Fernando Zacarías Flores, Dionicio Zacarías Flores, Rosalba Cuapa Canto, Luis Miguel Guzmán Muñoz

$37.50

Chapter 210

Solar Radiation Forecasting Model
(pages 1433-1438)

Fatih Onur Hocaoglu, Ömer Nezih Gerek, Mehmet Kurban

$37.50

Chapter 211

Speech-Based Clinical Diagnostic Systems
(pages 1439-1446)

Jesús Bernardino Alonso Hernández, Patricia Henríquez Rodríguez

$37.50

Chapter 212

State of the Art in Writer's Off-Line Identification
(pages 1447-1454)

Carlos M. Travieso González, Carlos F. Romero

$37.50

Chapter 213

State-of-the-Art on Video-Based Face Recognition
(pages 1455-1461)

Yan Yan, Yu-Jin Zhang

$37.50

Chapter 214

Stationary Density of Stochastic Search Processes
(pages 1462-1466)

Arturo Berrones, Dexmont Peña, Ricardo Sánchez

$37.50

Chapter 215

Statistical Modelling of Highly Inflective Languages
(pages 1467-1473)

Mirjam Sepesy Maucec, Zdravko Kacic

$37.50

Chapter 216

Statistical Simulations on Perceptron-Based Adders
(pages 1474-1481)

Snorre Aunet, Hans Kristian Otnes Berge

$37.50

$37.50

Chapter 218

Stream Processing of a Neural Classifier I
(pages 1490-1496)

M. Martínez-Zarzuela, F. J. Díaz Pernas, D. González Ortega, J. F. Díez Higuera, M. Antón Rodríguez

$37.50

Chapter 219

Stream Processing of a Neural Classifier II
(pages 1497-1503)

M. Martínez-Zarzuela, F. J. Díaz Pernas, D. González Ortega, J. F. Díez Higuera, M. Antón Rodríguez

$37.50

$37.50

$37.50

$37.50

Chapter 223

A Survey on Neural Networks in Automated Negotiations
(pages 1524-1529)

Ioannis Papaioannou, Ioanna Roussaki, Miltiades Anagnostou

$37.50

Chapter 224

Swarm Intelligence Approach for Ad-Hoc Networks
(pages 1530-1536)

Prayag Narula, Sudip Misra, Sanjay Kumar Dhurandher

$37.50

$37.50

$37.50

$37.50

$37.50

$37.50

Chapter 230

Thermal Design of Gas-Fired Cooktop Burners Through ANN
(pages 1568-1575)

T. T. Wong, C. W. Leung

$37.50

Chapter 231

A 2D Positioning Application in PET Using ANNs
(pages 1576-1582)

Fernando Mateo, Ramón J. Aliaga, Jorge D. Martínez, José Ma Monzó, Rafael Gadea

$37.50

Chapter 232

2D-PAGE Analysis Using Evolutionary Computation
(pages 1583-1588)

Pablo Mesejo, Enrique Fernández-Blanco, Diego Martínez-Feijóo, Francisco J. Blanco

$37.50

Chapter 233

Visualizing Cancer Databases Using Hybrid Spaces
(pages 1589-1595)

Julio J. Valdés, Alan J. Barton

$37.50

Chapter 234

Voltage Instability Detection Using Neural Networks
(pages 1596-1602)

Adnan Khashman, Kadri Buruncuk, Samir Jabr

$37.50

Chapter 235

Wave Reflection at Submerged Breakwaters
(pages 1603-1609)

Alberte Castro Ponte, Gregorio Iglesias, Francisco Taveira Pinto, Rodrigo Carballo

$37.50

Chapter 236

Web-Based Assessment System Applying Many-Valued Logic
(pages 1610-1614)

Sylvia Encheva, Sharil Tumin

$37.50

Chapter 237

Workflow Management Based on Mobile Agent Technology
(pages 1615-1623)

Marina Flores-Badillo, Ernesto López-Mellado

$37.50

About the Editors

Index