Constraint Programming (CP) has been successfully applied to both constraint satisfaction and constraint optimization problems. A wide variety of specialized global constraints provide critical assistance in achieving a good model that can take advantage of the structure of the problem in the search for a solution. However, a key outstanding issue is the representation of 'ad-hoc' constraints that do not have an inherent combinatorial nature, and hence are not modeled well using narrowly specialized global constraints. We attempt to address this issue by considering a hybrid of search and compilation. Specifically we suggest the use of Reduced Ordered Multi-Valued Decision Diagrams (ROMDDs) as the supporting data structure for a generic global constraint. We give an algorithm for maintaining generalized arc consistency (GAC) on this constraint that amortizes the cost of the GAC computation over a root-to-leaf path in the search tree without requiring asymptotically more space than used for the MDD. Furthermore we present an approach for incrementally maintaining the reduced property of the MDD during the search, and show how this can be used for providing domain entailment detection. Finally we discuss how to apply our approach to other similar data structures such as AOMDDs and Case DAGs. The technique used can be seen as an extension of the GAC algorithm for the regular language constraint on finite length input.
We study the relations between Multi-valued Decision Diagrams (MDD) and tuples (i.e. elements of the Cartesian Product of variables). First, we improve the existing methods for transforming a set of tuples, Global Cut Seeds, sequences of tuples into MDDs. Then, we present some in-place algorithms for adding and deleting tuples from an MDD. Next, we consider an MDD constraint which is modified during the search by deleting some tuples. We give an algorithm which adapts MDD-4R to these dynamic and persistent modifications. Some experiments show that MDD constraints are competitive with Table con…
University of Oran（奥兰大学）；EPSECG of Oran（奥兰高等经济与商业管理学院）；University of Caen（卡昂大学）；University PARIS 13（巴黎第十三大学）
Sequential pattern mining (SPM) under gap constraint is a challenging task. Many efficient specialized methods have been developed but they are all suffering from a lack of genericity. The Constraint Programming (CP) approaches are not so effective because of the size of their encodings. In[7], we have proposed the global constraint Prefix-Projection for SPM which remedies to this drawback. However, this global constraint cannot be directly extended to support gap constraint. In this paper, we propose the global constraint GAP-SEQ enabling to handle SPM with or without gap constraint. GAP-SEQ …
Preparatory school of Oran EPSECG（奥兰预备学校 EPSECG）；University of Oran 1（奥兰第一大学）；University of Caen（卡昂大学）；University PARIS 13（巴黎第十三大学）
Sequential pattern mining under constraints is a challenging data mining task. Many efficient ad hoc methods have been developed for mining sequential patterns, but they are all suffering from a lack of genericity. Recent works have investigated Constraint Programming (CP) methods, but they are not still effective because of their encoding. In this paper, we propose a global constraint based on the projected databases principle which remedies to this drawback. Experiments show that our approach clearly outperforms CP approaches and competes well with ad hoc methods on large datasets.
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…
The Complexity of Reasoning with Global Constraints
LIRMM, CNRS/U. Montpellier（法国国家科学研究中心/蒙彼利埃大学 朗格多克信息学、机器人学与微电子实验室）；C and UCC（科克大学 约束计算中心）；Izmir University of Economics（伊兹密尔经济大学）；NICTA and UNSW（澳大利亚国家信息与通信技术研究院 新南威尔士大学）
University of Oran 1（奥兰第一大学）；University of Montpellier（蒙彼利埃大学）；University of Caen（卡昂大学）
Discovering the set of closed frequent patterns is one of the fundamental problems in Data Mining. Recent Constraint Programming (CP) approaches for declarative itemset mining have proven their usefulness and flexibility. But the wide use of reified constraints in current CP approaches raises many difficulties to cope with high dimensional datasets. This paper proposes CLOSED PATTERN global constraint which does not require any reified constraints nor any extra variables to encode efficiently the Closed Frequent Pattern Mining (CFPM) constraint. CLOSED-PATTERN captures the particular semantics…
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…
Tokyo Institute of Technology（东京工业大学）；The University of Tokyo（东京大学）；IBM Watson Research Center（IBM沃森研究中心）；University College Dublin（都柏林大学学院）
We present a scalable parallel solver for numerical constraint satisfaction problems (NCSPs). Our parallelization scheme consists of homogeneous worker solvers, each of which runs on an available core and communicates with others via the global load balancing (GLB) method. The parallel solver is implemented with X10 that provides an implementation of GLB as a library. In experiments, several NCSPs from the literature were solved and attained up to 516-fold speedup using 600 cores of the TSUBAME2.5 supercomputer.
Every Constraint Programming (CP) solver exposes a library of constraints for solving combinatorial problems. In order to be useful, CP solvers need to be bug-free. Therefore the testing of the solver is crucial to make developers and users confident. We present a Java library allowing any JVM based solver to test that the implementations of the individual constraints are correct. The library can be used in a test suite executed in a continuous integration tool or it can also be used to discover minimalist instances violating some properties (arc-consistency, etc) in order to help the develope…
Filtering Algorithms for the Multiset Ordering Constraint
University of York（约克大学）；Izmir University of Economics（伊兹密尔经济大学）；University of Bologna（博洛尼亚大学）；University of St Andrews（圣安德鲁斯大学）；NICTA（澳大利亚国家信息通信技术研究院）；University of New South Wales（新南威尔士大学）
IMT Atlantique（大西洋国立高等矿业电信学院）；RISE SICS（瑞典计算机科学研究院（RISE旗下））；Uppsala University（乌普萨拉大学）；National University of Singapore（新加坡国立大学）；University College Cork（科克大学）
First this report presents a restricted set of finite transducers used to synthesise structural time-series constraints described by means of a multi-layered function composition scheme. Second it provides the corresponding synthesised catalogue of structural time-series constraints where each constraint is explicitly described in terms of automata with registers.
Gala: Global LLM Agents for Text-to-Model Translation
Department of Computer Science, University of Southern California（南加州大学计算机科学系）；AI Center of Excellence, Fidelity Investments（富达投资人工智能卓越中心）；Department of Computer Science, Brown University（布朗大学计算机科学系）
Open forms of global constraints allow the addition of new variables to an argument during the execution of a constraint program. Such forms are needed for difficult constraint programming problems where problem construction and problem solving are interleaved, and fit naturally within constraint logic programming. However, in general, filtering that is sound for a global constraint can be unsound when the constraint is open. This paper provides a simple characterization, called contractibility, of the constraints where filtering remains sound when the constraint is open. With this characteriz…
TU Dresden（德累斯顿工业大学）；University of Wrocław（弗罗茨瓦夫大学）
We introduce and investigate the expressive description logic (DL) ALCSCC++, in which the global and local cardinality constraints introduced in previous papers can be mixed. On the one hand, we prove that this does not increase the complexity of satisfiability checking and other standard inference problems. On the other hand, the satisfiability problem becomes undecidable if inverse roles are added to the languages. In addition, even without inverse roles, conjunctive query entailment in this DL turns out to be undecidable. We prove that decidability of querying can be regained if global and …
We propose a universal Graph Neural Network architecture which can be trained as an end-2-end search heuristic for any Constraint Satisfaction Problem (CSP). Our architecture can be trained unsupervised with policy gradient descent to generate problem specific heuristics for any CSP in a purely data driven manner. The approach is based on a novel graph representation for CSPs that is both generic and compact and enables us to process every possible CSP instance with one GNN, regardless of constraint arity, relations or domain size. Unlike previous RL-based methods, we operate on a global searc…
