LIRMM；CNRS（法国国家科学研究中心）；CRIL-CNRS（CRIL-法国国家科学研究中心）；NICTA（澳大利亚国家信息与通信技术研究院）；University of NSW（新南威尔士大学）；Université Laval（拉瓦尔大学）
Christian Bessiere, George Katsirelos, Nina Narodytska, Claude-Guy Quimper, Toby Walsh
备注：
To appear in the Proceedings of the 16th International Conference on Principles and Practice of Constraint Programming 2010 (CP 2010). An earlier version appeared in the Proceedings of the Eighth International Workshop on Constraint Modelling and Reformulation, held alongside the 15th International Conference on Principles and Practice of Constraint Programming (CP 2009)
We study decompositions of the global NVALUE constraint. Our main contribution is theoretical: we show that there are propagators for global constraints like NVALUE which decomposition can simulate with the same time complexity but with a much greater space complexity. This suggests that the benefit of a global propagator may often not be in saving time but in saving space. Our other theoretical contribution is to show for the first time that range consistency can be enforced on NVALUE with the same worst-case time complexity as bound consistency. Finally, the decompositions we study are readily encoded as linear inequalities. We are therefore able to use them in integer linear programs.
LIRMM；CNRS（法国国家科学研究中心）；NICTA（国家信息与通信技术研究院）；University of NSW（新南威尔士大学）；École Polytechnique de Montréal（蒙特利尔综合理工学院）
We study decompositions of NVALUE, a global constraint that can be used to model a wide range of problems where values need to be counted. Whilst decomposition typically hinders propagation, we identify one decomposition that maintains a global view as enforcing bound consistency on the decomposition achieves bound consistency on the original global NVALUE constraint. Such decompositions offer the prospect for advanced solving techniques like nogood learning and impact based branching heuristics. They may also help SAT and IP solvers take advantage of the propagation of global constraints.
Bessiere et al. (AAAI'08) showed that several intractable global constraints can be efficiently propagated when certain natural problem parameters are small. In particular, the complete propagation of a global constraint is fixed-parameter tractable in k - the number of holes in domains - whenever bound consistency can be enforced in polynomial time; this applies to the global constraints AtMost-NValue and Extended Global Cardinality (EGC). In this paper we extend this line of research and introduce the concept of reduction to a problem kernel, a key concept of parameterized complexity, to the…
UNSW Australia（新南威尔士大学）；NICTA（澳大利亚国家信息与通信技术研究院）；Vienna University of Technology（维也纳工业大学）
We present a first theoretical analysis of the power of polynomial-time preprocessing for important combinatorial problems from various areas in AI. We consider problems from Constraint Satisfaction, Global Constraints, Satisfiability, Nonmonotonic and Bayesian Reasoning under structural restrictions. All these problems involve two tasks: (i) identifying the structure in the input as required by the restriction, and (ii) using the identified structure to solve the reasoning task efficiently. We show that for most of the considered problems, task (i) admits a polynomial-time preprocessing to a …
We show that some common and important global constraints like ALL-DIFFERENT and GCC can be decomposed into simple arithmetic constraints on which we achieve bound or range consistency, and in some cases even greater pruning. These decompositions can be easily added to new solvers. They also provide other constraints with access to the state of the propagator by sharing of variables. Such sharing can be used to improve propagation between constraints. We report experiments with our decomposition in a pseudo-Boolean solver.
We describe decomposition during search (DDS), an integration of And/Or tree search into propagation-based constraint solvers. The presented search algorithm dynamically decomposes sub-problems of a constraint satisfaction problem into independent partial problems, avoiding redundant work. The paper discusses how DDS interacts with key features that make propagation-based solvers successful: constraint propagation, especially for global constraints, and dynamic search heuristics. We have implemented DDS for the Gecode constraint programming library. Two applications, solution counting in graph…
Relax, Compensate and then Recover (RCR) is a paradigm for approximate inference in probabilistic graphical models that has previously provided theoretical and practical insights on iterative belief propagation and some of its generalizations. In this paper, we characterize the technique of dual decomposition in the terms of RCR, viewing it as a specific way to compensate for relaxed equivalence constraints. Among other insights gathered from this perspective, we propose novel heuristics for recovering relaxed equivalence constraints with the goal of incrementally tightening dual decomposition…
A wide range of problems can be modelled as constraint satisfaction problems (CSPs), that is, a set of constraints that must be satisfied simultaneously. Constraints can either be represented extensionally, by explicitly listing allowed combinations of values, or implicitly, by special-purpose algorithms provided by a solver. Such implicitly represented constraints, known as global constraints, are widely used; indeed, they are one of the key reasons for the success of constraint programming in solving real-world problems. In recent years, a variety of restrictions on the structure of CSP inst…
CENTRIA - Centre for Artificial Intelligence（人工智能中心）；FCT/UNL（新里斯本大学科学技术学院）
Constraints that may be obtained by composition from simpler constraints are present, in some way or another, in almost every constraint program. The decomposition of such constraints is a standard technique for obtaining an adequate propagation algorithm from a combination of propagators designed for simpler constraints. The decomposition approach is appealing in several ways. Firstly because creating a specific propagator for every constraint is clearly infeasible since the number of constraints is infinite. Secondly, because designing a propagation algorithm for complex constraints can be v…
CNRS（法国国家科学研究中心）；LIRMM（蒙彼利埃信息、机器人与微电子实验室）；NICTA（澳大利亚国家信息与通信技术研究院）；University of NSW（新南威尔士大学）；Université Laval（拉瓦尔大学）
We propose AllDiffPrecedence, a new global constraint that combines together an AllDifferent constraint with precedence constraints that strictly order given pairs of variables. We identify a number of applications for this global constraint including instruction scheduling and symmetry breaking. We give an efficient propagation algorithm that enforces bounds consistency on this global constraint. We show how to implement this propagator using a decomposition that extends the bounds consistency enforcing decomposition proposed for the AllDifferent constraint. Finally, we prove that enforcing d…
University of Lethbridge（莱斯布里奇大学）；InBridge Inc（英桥公司）
We study the design of stochastic local search methods to prove unsatisfiability of a constraint satisfaction problem (CSP). For a binary CSP, such methods have been designed using the microstructure of the CSP. Here, we develop a method to decompose the microstructure into graph tensors. We show how to use the tensor decomposition to compute a proof of unsatisfiability efficiently and in parallel. We also offer substantial empirical evidence that our approach improves the praxis. For instance, one decomposition yields proofs of unsatisfiability in half the time without sacrificing the quality…
Constraint Satisfaction Problems (CSPs) play a central role in many applications in Artificial Intelligence and Operations Research. In general, solving CSPs is NP-complete. The structure of CSPs is best described by hypergraphs. Therefore, various forms of hypergraph decompositions have been proposed in the literature to identify tractable fragments of CSPs. However, also the computation of a concrete hypergraph decomposition is a challenging task in itself. In this paper, we report on recent progress in the study of hypergraph decompositions and we outline several directions for future resea…
We show that tools from circuit complexity can be used to study decompositions of global constraints. In particular, we study decompositions of global constraints into conjunctive normal form with the property that unit propagation on the decomposition enforces the same level of consistency as a specialized propagation algorithm. We prove that a constraint propagator has a a polynomial size decomposition if and only if it can be computed by a polynomial size monotone Boolean circuit. Lower bounds on the size of monotone Boolean circuits thus translate to lower bounds on the size of decompositi…
Ecole Polytechnique de Montréal（蒙特利尔理工学院）；NICTA（澳大利亚国家信息与通信技术研究院）；UNSW（新南威尔士大学）
A wide range of constraints can be compactly specified using automata or formal languages. In a sequence of recent papers, we have shown that an effective means to reason with such specifications is to decompose them into primitive constraints. We can then, for instance, use state of the art SAT solvers and profit from their advanced features like fast unit propagation, clause learning, and conflict-based search heuristics. This approach holds promise for solving combinatorial problems in scheduling, rostering, and configuration, as well as problems in more diverse areas like bioinformatics, s…
The general intractability of the constraint satisfaction problem has motivated the study of restrictions on this problem that permit polynomial-time solvability. One major line of work has focused on structural restrictions, which arise from restricting the interaction among constraint scopes. In this paper, we engage in a mathematical investigation of generalized hypertree width, a structural measure that has up to recently eluded study. We obtain a number of computational results, including a simple proof of the tractability of CSP instances having bounded generalized hypertree width.
Structural decomposition methods, such as generalized hypertree decompositions, have been successfully used for solving constraint satisfaction problems (CSPs). As decompositions can be reused to solve CSPs with the same constraint scopes, investing resources in computing good decompositions is beneficial, even though the computation itself is hard. Unfortunately, current methods need to compute a completely new decomposition even if the scopes change only slightly. In this paper, we make the first steps toward solving the problem of updating the decomposition of a CSP $P$ so that it becomes a…
Stanford University（斯坦福大学）；Cornell University（康奈尔大学）；Joint Center for Artificial Photosynthesis（人工光合作用联合中心）；California Institute of Technology（加州理工学院）
Identifying important components or factors in large amounts of noisy data is a key problem in machine learning and data mining. Motivated by a pattern decomposition problem in materials discovery, aimed at discovering new materials for renewable energy, e.g. for fuel and solar cells, we introduce CombiFD, a framework for factor based pattern decomposition that allows the incorporation of a-priori knowledge as constraints, including complex combinatorial constraints. In addition, we propose a new pattern decomposition algorithm, called AMIQO, based on solving a sequence of (mixed-integer) quad…
Segmenting dental plaque from images of medical reagent staining provides valuable information for diagnosis and the determination of follow-up treatment plan. However, accurate dental plaque segmentation is a challenging task that requires identifying teeth and dental plaque subjected to semantic-blur regions (i.e., confused boundaries in border regions between teeth and dental plaque) and complex variations of instance shapes, which are not fully addressed by existing methods. Therefore, we propose a semantic decomposition network (SDNet) that introduces two single-task branches to separatel…
The goal of this paper is to set a constraint programming framework to solve lot-sizing problems. More specifically, we consider a single-item lot-sizing problem with time-varying lower and upper bounds for production and inventory. The cost structure includes time-varying holding costs, unitary production costs and setup costs. We establish a new lower bound for this problem by using a subtle time decomposition. We formulate this NP-hard problem as a global constraint and show that bound consistency can be achieved in pseudo-polynomial time and when not including the costs, in polynomial time…
University of Edinburgh（爱丁堡大学）；University of Saint Andrews（圣安德鲁斯大学）；University College Cork（科克大学学院）；Cankaya University（昌卡亚大学）
We introduce the BIN_COUNTS constraint, which deals with the problem of counting the number of decision variables in a set which are assigned values that lie in given bins. We illustrate a decomposition and a filtering algorithm that achieves generalised arc consistency. We contrast the filtering power of these two approaches and we discuss a number of applications. We show that BIN_COUNTS can be employed to develop a decomposition for the $χ^2$ test constraint, a new statistical constraint that we introduce in this work. We also show how this new constraint can be employed in the context of t…
Navigating the Proximity-Safety Balance: Constraint Decomposition for Human Following in Pedestrian Crowds
University of Pennsylvania（宾夕法尼亚大学）；University of California, Riverside（加州大学河滨分校）；Stanford University（斯坦福大学）；NVIDIA Research（英伟达研究院）；Georgia Institute of Technology（佐治亚理工学院）
