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119
Increasing Constraint Propagation by Redundant Modeling: an Experience Report
 CONSTRAINTS
, 1999
"... This paper describes our experience with a simple modeling and programming approach for increasing the amount of constraint propagation in the constraint solving process. The idea, although similar to redundant constraints, is based on the concept of redundant modeling. We introduce the notions of ..."
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Cited by 74 (8 self)
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This paper describes our experience with a simple modeling and programming approach for increasing the amount of constraint propagation in the constraint solving process. The idea, although similar to redundant constraints, is based on the concept of redundant modeling. We introduce the notions of CSP model and model redundancy, and show how mutually redundant models can be combined and connected using channeling constraints. The combined model contains the mutually redundant models as submodels. Channeling constraints allow the submodels to cooperate during constraint solving by propagating constraints freely amongst the submodels. This extra level of pruning and propagation activities becomes the source of execution speedup. We perform two case studies to evaluate the effectiveness and efficiency of our method. The first case study is based on the simple and wellknown nqueens problem, while the second case study applies our method in the design and construction of a reallife ...
Cp(graph): Introducing a graph computation domain in constraint programming
 In CP2005 Proceedings
, 2005
"... Abstract. In an increasing number of domains such as bioinformatics, combinatorial graph problems arise. We propose a novel way to solve these problems, mainly those that can be translated to constrained subgraph finding. Our approach extends constraint programming by introducing CP(Graph), a new co ..."
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Cited by 52 (12 self)
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Abstract. In an increasing number of domains such as bioinformatics, combinatorial graph problems arise. We propose a novel way to solve these problems, mainly those that can be translated to constrained subgraph finding. Our approach extends constraint programming by introducing CP(Graph), a new computation domain focused on graphs including a new type of variable: graph domain variables as well as constraints over these variables and their propagators. These constraints are subdivided into kernel constraints and additional constraints formulated as networks of kernel constraints. For some of these constraints a dedicated global constraint and its associated propagator are sketched. CP(Graph) is integrated with finite domain and finite sets computation domains, allowing the combining of constraints of these domains with graph constraints. A prototype of CP(Graph) built over finite domains and finite sets in Oz is presented. And we show that a problem of biochemical network analysis can be very simply described and solved within CP(Graph). 1
Function Variables for Constraint Programming
, 2003
"... We introduce function variables to constraint programs (CP), variables whose values are one of (exponentially many) possible functions between two sets. Such variables are useful for modelling problems from domains such as configuration, planning, scheduling, etc. We show that a function variable ca ..."
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Cited by 40 (5 self)
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We introduce function variables to constraint programs (CP), variables whose values are one of (exponentially many) possible functions between two sets. Such variables are useful for modelling problems from domains such as configuration, planning, scheduling, etc. We show that a function variable can be mapped into different representations in terms of integer and set variables, and illustrate how to map constraints stated on a function variable into constraints on integer and set variables. As a result, a constraint model expressed using function variables allows for the generation of alternate CP models. Furthermore, we present an extensive theoretical comparison of models of problems involving injective functions supported by asymptotic and empirical studies. Finally, we present and evaluate a practical modelling tool that is based on a highlevel language that supports function variables. The tool helps users explore different alternate CP models starting from a function model that is easy to develop, understand, and maintain.
Solving the Kirkman's Schoolgirl Problem in a Few Seconds
 In Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
, 2002
"... The Social Golfer Problem has been extensively used in recent years by the constraint community as an example of highly symmetric problem. It is an excellent problem for benchmarking symmetry breaking mechanisms such as SBDS or SBDD and for demonstrating the importance of the choice of the right mod ..."
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Cited by 34 (0 self)
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The Social Golfer Problem has been extensively used in recent years by the constraint community as an example of highly symmetric problem. It is an excellent problem for benchmarking symmetry breaking mechanisms such as SBDS or SBDD and for demonstrating the importance of the choice of the right model for one problem. We address in this paper a specific instance of the Golfer Problem well known as the Kirkman's Schoolgirl Problem and list a collection of techniques and tricks to find efficiently all its unique solutions. In particular, we propose SBDD+, an generic improvement over SBDD which allows a deep pruning when a symmetry is detected during the search. Our implementation of the presented techniques allows us to improve previous published results by an order of magnitude for CPU time as well as number of backtracks, and to compute the seven unique solutions of the Kirkman's problem in a few seconds.
Solving set constraint satisfaction problems using ROBDDs
 Journal of Artificial Intelligence Research
, 2005
"... In this paper we present a new approach to modeling finite set domain constraint problems using Reduced Ordered Binary Decision Diagrams (ROBDDs). We show that it is possible to construct an efficient set domain propagator which compactly represents many set domains and set constraints using ROBDDs. ..."
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Cited by 32 (4 self)
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In this paper we present a new approach to modeling finite set domain constraint problems using Reduced Ordered Binary Decision Diagrams (ROBDDs). We show that it is possible to construct an efficient set domain propagator which compactly represents many set domains and set constraints using ROBDDs. We demonstrate that the ROBDDbased approach provides unprecedented flexibility in modeling constraint satisfaction problems, leading to performance improvements. We also show that the ROBDDbased modeling approach can be extended to the modeling of integer and multiset constraint problems in a straightforward manner. Since domain propagation is not always practical, we also show how to incorporate less strict consistency notions into the ROBDD framework, such as set bounds, cardinality bounds and lexicographic bounds consistency. Finally, we present experimental results that demonstrate the ROBDDbased solver performs better than various more conventional constraint solvers on several standard set constraint problems. 1.
Global constraints for integer and set value precedence
 In: Proceedings of 10th International Conference on Principles and Practice of Constraint Programming (CP2004
, 2004
"... Abstract. The paper introduces value precedence on integer and set sequences. A useful application of the notion is in breaking symmetries of indistinguishable values, an important class of symmetries in practice. Although value precedence can be expressed straightforwardly using ifthen constraint ..."
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Cited by 30 (2 self)
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Abstract. The paper introduces value precedence on integer and set sequences. A useful application of the notion is in breaking symmetries of indistinguishable values, an important class of symmetries in practice. Although value precedence can be expressed straightforwardly using ifthen constraints in existing constraint programming systems, the resulting formulation is inefficient both in terms of size and runtime. We present two propagation algorithms for implementing global constraints on value precedence in the integer and set domains. Besides conducting experiments to verify the feasibility and efficiency of our proposal, we characterize also the propagation level attained by various usages of the global constraints as well as the conditions when the constraints can be used consistently with other types of symmetry breaking constraints.
Finite set constraints in Oz
 TECHNISCHE UNIVERSITÄT MÜNCHEN
, 1997
"... We report on the extension of the concurrent constraint language Oz by constraints over finite sets of integers. Set constraints are an important addition to the constraint programming system Oz and are very employable in natural language processing and general problem solving. This extension profit ..."
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Cited by 27 (4 self)
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We report on the extension of the concurrent constraint language Oz by constraints over finite sets of integers. Set constraints are an important addition to the constraint programming system Oz and are very employable in natural language processing and general problem solving. This extension profits much from its integration with the existing constraint systems over finite domains and feature trees, as well as from the availability of firstclass procedures. This combination of features is unique to Oz. This paper focuses on the expressiveness gained by set constraints and on the benefits of the integration with finite domain constraints. A number of case studies demonstrates programming techniques exploring these advantages.
Views and iterators for generic constraint implementations
 In Recent Advances in Constraints (2005
, 2005
"... Abstract. This paper introduces an architecture for generic constraint implementations based on variable views and range iterators. Views allow, for example, to scale, translate, and negate variables. The paper shows how to make constraint implementations generic and how to reuse a single generic im ..."
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Cited by 24 (2 self)
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Abstract. This paper introduces an architecture for generic constraint implementations based on variable views and range iterators. Views allow, for example, to scale, translate, and negate variables. The paper shows how to make constraint implementations generic and how to reuse a single generic implementation with different views for different constraints. A wide range of applications of views exemplifies their usefulness and their potential for simplifying constraint implementations. We introduce domain operations compatible with views based on range iterators. The paper evaluates the applicability of the approach as well as different implementation techniques for the presented architecture. 1
Dominance Constraints with Set Operators
 In Proceedings of the First International Conference on Computational Logic (CL2000), LNCS
, 2000
"... Dominance constraints are widely used in computational linguistics as a language for talking and reasoning about trees. In this paper, we extend dominance constraints by admitting set operators. We present a solver for dominance constraints with set operators, which is based on propagation and d ..."
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Cited by 23 (16 self)
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Dominance constraints are widely used in computational linguistics as a language for talking and reasoning about trees. In this paper, we extend dominance constraints by admitting set operators. We present a solver for dominance constraints with set operators, which is based on propagation and distribution rules, and prove its soundness and completeness.