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22
Encodings of NonBinary Constraint Satisfaction Problems
, 1999
"... We perform a detailed theoretical and empirical comparison of the dual and hidden variable encodings of nonbinary constraint satisfaction problems. We identify a simple relationship between the two encodings by showing how we can translate between the two by composing or decomposing relations. ..."
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Cited by 47 (10 self)
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We perform a detailed theoretical and empirical comparison of the dual and hidden variable encodings of nonbinary constraint satisfaction problems. We identify a simple relationship between the two encodings by showing how we can translate between the two by composing or decomposing relations. This translation
Partition Search for Nonbinary Constraint Satisfaction
 Information Sciences
, 2007
"... Previous algorithms for unrestricted constraint satisfaction use reduction search, which inferentially removes values from domains in order to prune the backtrack search tree. This paper introduces partition search, which uses an efficient join mechanism instead of removing values from domains. Anal ..."
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Cited by 18 (0 self)
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Previous algorithms for unrestricted constraint satisfaction use reduction search, which inferentially removes values from domains in order to prune the backtrack search tree. This paper introduces partition search, which uses an efficient join mechanism instead of removing values from domains. Analytical prediction of quantitative performance of partition search appears to be intractable and evaluation therefore has to be by experimental comparison with reduction search algorithms that represent the state of the art. Instead of working only with available reduction search algorithms, this paper introduces enhancements such as semijoin reduction preprocessing using Bloom filtering.
Integrating CSP Decomposition Techniques and BDDs for Compiling Configuration Problems
 In Proceedings of the CPAIOR. Springer LNCS
, 2005
"... In this project we present, the treeofBDDs approach, a decomposition scheme for compiling configuration problems. We also present efficient techniques for generating minimum explanations in the BDDbased configuration schemes. Given a BDD representing the solutions of a CSP, an efficient technique ..."
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Cited by 16 (1 self)
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In this project we present, the treeofBDDs approach, a decomposition scheme for compiling configuration problems. We also present efficient techniques for generating minimum explanations in the BDDbased configuration schemes. Given a BDD representing the solutions of a CSP, an efficient technique for detecting full interchangeable values is given. Experimental results show that the techniques presented here drastically reduces the time and space requirements for interactive configurators.
Efficient Reasoning for Nogoods in Constraint Solvers with BDDs
"... Abstract. When BDDs are used for propagation in a constraint solver with nogood recording, it is necessary to find a small subset of a given set of variable assignments that is enough for a BDD to imply a new variable assignment. We show that the task of finding such a minimum subset is NPcomplete ..."
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Cited by 6 (0 self)
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Abstract. When BDDs are used for propagation in a constraint solver with nogood recording, it is necessary to find a small subset of a given set of variable assignments that is enough for a BDD to imply a new variable assignment. We show that the task of finding such a minimum subset is NPcomplete by reduction from the hitting set problem. We present a new algorithm for finding such a minimal subset, which runs in time linear in the size of the BDD representation. In our experiments, the new method is up to ten times faster than the previous method, thereby reducing the solution time by even more than 80%. Due to linear time complexity the new method is able to scale well. 1
Interactive Cost Configuration Over Decision Diagrams
 Journal of Artificial Intelligence Research (JAIR
"... Abstract In many AI domains such as product configuration, a user should interactively specify a solution that must satisfy a set of constraints. In such scenarios, offline compilation of feasible solutions into a tractable representation is an important approach to delivering efficient backtrackf ..."
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Abstract In many AI domains such as product configuration, a user should interactively specify a solution that must satisfy a set of constraints. In such scenarios, offline compilation of feasible solutions into a tractable representation is an important approach to delivering efficient backtrackfree user interaction online. In particular, binary decision diagrams (BDDs) have been successfully used as a compilation target for product and service configuration. In this paper we discuss how to extend BDDbased configuration to scenarios involving cost functions which express user preferences. We first show that an efficient, robust and easy to implement extension is possible if the cost function is additive, and feasible solutions are represented using multivalued decision diagrams (MDDs). We also discuss the effect on MDD size if the cost function is nonadditive or if it is encoded explicitly into MDD. We then discuss interactive configuration in the presence of multiple cost functions. We prove that even in its simplest form, multiplecost configuration is NPhard in the input MDD. However, for solving twocost configuration we develop a pseudopolynomial scheme and a fully polynomial approximation scheme. The applicability of our approach is demonstrated through experiments over realworld configuration models and productcatalogue datasets. Response times are generally within a fraction of a second even for very large instances.
Calculating valid domains for bddbased interactive configuration
, 2007
"... Abstract. In these notes we formally describe the functionality of Calculating Valid Domains from the BDD representing the solution space of valid configurations. The formalization is largely based on the CLab [1] configuration framework. 1 ..."
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Cited by 5 (0 self)
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Abstract. In these notes we formally describe the functionality of Calculating Valid Domains from the BDD representing the solution space of valid configurations. The formalization is largely based on the CLab [1] configuration framework. 1
Combining binary decision diagrams and backtracking search for scalable backtrackfree interactive product configuration
 in In Proceedings of the IJCAI09 Workshop on Configuration
, 2000
"... This paper demonstrates how to create approximations of a configuration problem using BDDs to improve performance over a pure searchbased configurator, for problems that are intractable to represent by a monolithic BDD. The paper demonstrates several ways to build the approximations and it sho ..."
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Cited by 4 (1 self)
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This paper demonstrates how to create approximations of a configuration problem using BDDs to improve performance over a pure searchbased configurator, for problems that are intractable to represent by a monolithic BDD. The paper demonstrates several ways to build the approximations and it shows that using search results for building and improving the approximations leads to a significant performance gain. 1
Linear functions for interactive configuration using join matching and CSP tree decomposition
 Water Utilities Partnership. 2000. &quot;Draft Report on Status of Reforms of the Water and Sanitation Sector in Africa.&quot; Water Utilities Partnership: Abidjan, Côte d'Ivoire
, 2005
"... Quick responses are required for interactive configuration. For this an ideal interactive configurator needs to provide the functionalities required for interactive configuration with at most linear time complexity. In this paper, we present such a data structure called Join Matched CSP (JMCSP). Whe ..."
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Cited by 4 (0 self)
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Quick responses are required for interactive configuration. For this an ideal interactive configurator needs to provide the functionalities required for interactive configuration with at most linear time complexity. In this paper, we present such a data structure called Join Matched CSP (JMCSP). When a JMCSP is used to represent a configuration problem, the functionalities required for interactive configuration can be obtained with linear time complexity. Unlike the treeofBDDs [Subbarayan, 2005], the JMCSPs while taking advantage of treedecomposition also provide linear configuration functions. Although obtaining a JMCSP is exponential in the treewidth of the input configuration problem, due to treelike hierarchical nature of configuration problems, this is typically feasible. We present the JMCSP compilation process along with the linear interactive configuration functions on it. The linear functionalities provided by the JMCSPs include computation of all minimum explanations. 1
Techniques for efficient interactive configuration of distribution networks
 In Proc. 20th International Joint Conference on Artificial Intelligence (IJCAI
, 2007
"... Recovering from power outages is an essential task in distribution of electricity. Our industrial partner postulates that the recovery should be interactive rather than automatic: supporting the operator by preventing choices that destabilize the network. Interactive configurators, successfully used ..."
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Cited by 4 (0 self)
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Recovering from power outages is an essential task in distribution of electricity. Our industrial partner postulates that the recovery should be interactive rather than automatic: supporting the operator by preventing choices that destabilize the network. Interactive configurators, successfully used in specifying products and services, support users in selecting logically constrained parameters in a sound, complete and backtrackfree manner. Interactive restoration algorithms based on reduced ordered binary decision diagrams (BDDs) had been developed also for power distribution networks, however they did not scale to the large instances, as BDDs representing these could not be compiled. We discuss the theoretical hardness of the interactive configuration and then provide techniques used to compile two classes of networks. We handle the largest industrial instances available. Our techniques rely on symbolic reachability computation, early variable quantification, domain specific ordering heuristics and conjunctive decomposition. 1