Table Constraints Research Articles

Encoding Constraints as Binary Constraint Networks Satisfying BTP

Recently, the Binary Constraint Tree (BCT), a tree structured Binary Constraint Network (BCN), has been shown to be more succinct than various ad-hoc constraints. In this paper, we investigate the modelling power of a well-known tractable hybrid class generalizing BCT, i.e. the class of BCNs satisfying Broken Triangle Property (BTP) called BTP Networks (BTPNs). We show that the consistency checker of BTPN can be computed by polysize monotone circuit, thus, some global constraints cannot be encoded as polysize BTPN, such as the AllDifferent and Linear constraints. Then our study reveals that BTPN is strictly more succinct than the DNNF constraint and all 14 ad-hoc constraints discussed in (Wang and Yap 2023), such as the context-free grammar, BCT and smart table constraints. Furthermore, we also show that BTPN is as powerful as DNNF in terms of computing various operations and queries. In addition, we prove that it is NP-hard to determine the minimum sized BTPN encoding a constraint.

Ferry: Toward Better Understanding of Input/Output Space for Data Wrangling Scripts.

Understanding the input and output of data wrangling scripts is crucial for various tasks like debugging code and onboarding new data. However, existing research on script understanding primarily focuses on revealing the process of data transformations, lacking the ability to analyze the potential scope, i.e., the space of script inputs and outputs. Meanwhile, constructing input/output space during script analysis is challenging, as the wrangling scripts could be semantically complex and diverse, and the association between different data objects is intricate. To facilitate data workers in understanding the input and output space of wrangling scripts, we summarize ten types of constraints to express table space and build a mapping between data transformations and these constraints to guide the construction of the input/output for individual transformations. Then, we propose a constraint generation model for integrating table constraints across multiple transformations. Based on the model, we develop Ferry, an interactive system that extracts and visualizes the data constraints describing the input and output space of data wrangling scripts, thereby enabling users to grasp the high-level semantics of complex scripts and locate the origins of faulty data transformations. Besides, Ferry provides example input and output data to assist users in interpreting the extracted constraints and checking and resolving the conflicts between these constraints and any uploaded dataset. Ferry's effectiveness and usability are evaluated through two usage scenarios and two case studies, including understanding, debugging, and checking both single and multiple scripts, with and without executable data. Furthermore, an illustrative application is presented to demonstrate Ferry's flexibility.

Finding dependencies in data based on methods of satisfying table con-straints

The work deals with the search for a special type of regularities in data, called frequent patterns. A frequent pattern is understood as a certain set of attributes that characterizes a sufficiently large number of objects of the training sample. There are many methods for pattern discovery, but they usually do not allow flexible consideration of necessary requirements for their type. Taking into account the new conditions that the desired patterns must meet leads in practice to a time-consuming modification of used algorithms and a decrease in computing performance. This article proposes a new approach based on the constraint programming paradigm, which is free from the listed disadvantages. The approach is based on the original way of presenting the training sample using specialized table constraints – compressed D-type tables, on the author's method of backtracking, as well as on specialized reduction rules for table constraints. Particular attention is paid to solving the closed patterns discovery problem, which is included as part of the solution of all machine learning problems considered in the work, which means taking into account additional requirements for the type of patterns. As additional requirements to the type of pattern, constraints on the frequency of occurrence of a closed pattern, as well as conditions for the occurrence of some element (attribute) into the pattern, are considered. To the basic rules for the reduction of compressed D-type tables, rules are added that take into account the interesting attributes of the analyzed patterns. The advantage of the approach is that the taking into account and analyzing new constraints makes it possible to speed up the calculation process.

Correction to: Solution sampling with random table constraints

Correction to: Solution sampling with random table constraints

Graph constraints refined for transitive relations

As a powerful modelling tool, Constraint Satisfaction Problems (CSPs) can be solved efficiently using various solving paradigms and can encapsulate various types of constraints in a single model. Graph constraints are one such type of constraint. Existing graph constraints are dedicated to solve classical problems, such as constrained path problems and subgraph extraction problems. However, in some scenarios modelled with CSPs, there are relations where a formal path is formed by selecting a set of vertices on a graph, and the shortest path between two neighbouring vertices on that path needs to be restricted. Such relations are known as transitive relations on the graph, which cannot be expressed by existing graph constraints. Although expressive table constraints can be used to express transitive relations, this approach significantly reduces the performance of using table constraints. Therefore, to express transitive relations on a graph that can be efficiently modelled and reasoned by various types of CSP solvers, we propose two new constraints and present propagation algorithms based on generalized arc consistency. Finally, we perform comparative experiments to demonstrate the correctness and efficiency of the proposed approach. The results of the experiments not only prove the correctness of the propagation algorithms but also show that our proposed approach of modelling directly using new constraints and then reasoning using proprietary propagation algorithms, is more efficient than translating relations into table constraints and then reasoning.

An efficient heuristic approach combining maximal itemsets and area measure for compressing voluminous table constraints

Constraint Programming is a powerful paradigm to model and solve combinatorial problems. While there are many kinds of constraints, the table constraint is perhaps the most significant—being the most well-studied and has the ability to encode any other constraints defined on finite variables. However, constraints can be very voluminous and their size can grow exponentially with their arity. To reduce space and the time complexity, researchers have focused on various forms of compression. In this paper, we propose a new approach based on maximal frequent itemsets technique and area measure for enumerating the maximal frequent itemsets relevant for compressing table constraints. Our experimental results show the effectiveness and efficiency of this approach on compression and on solving compressed constraint satisfaction problem.

Encoding Multi-Valued Decision Diagram Constraints as Binary Constraint Trees

Ordered Multi-valued Decision Diagram (MDD) is a compact representation used to model various constraints, such as regular constraints and table constraints. It can be particularly useful for representing ad-hoc problem specific constraints. Many algorithms have been proposed to enforce Generalized Arc Consistency (GAC) on MDD constraints. In this paper, we introduce a new compact representation called Binary Constraint Tree (BCT). We propose tree binary encodings to transform any MDD constraint into a BCT constraint. We also present a specialized algorithm enforcing GAC on the BCT constraint resulting from a MDD constraint. Experimental results on a large set of benchmarks show that the BCT GAC algorithm can significantly outperform state-of-the-art MDD as well as table GAC algorithms.

Solution sampling with random table constraints

Constraint programming provides generic techniques to efficiently solve combinatorial problems. In this paper, we tackle the natural question of using constraint solvers to sample combinatorial problems in a generic way. We propose an algorithm, inspired from Meel’s ApproxMC algorithm on SAT, to add hashing constraints to a CP model in order to split the search space into small cells. By uniformly sampling the solutions in one cell, we can generate random solutions without revamping the model of the problem. We ensure the randomness by introducing a new family of hashing constraints: randomly generated tables, which keeps the cost of the hashing process tractable. We implemented this solving method using the constraint solver Choco-solver. The quality of the randomness and the running time of our approach are experimentally compared to a random branching strategy. We show that our approach improves the randomness while being in the same order of magnitude in terms of running time. We also use our algorithm with an other, more powerful, set of hashing constraints: linear modular equalities. We experimentally show that the resulting sampling is uniform, at the cost of a longer running time.

An Efficient Higher-Order Consistency Algorithm for Table Constraints

Table constraints are very important in constraint programming as they are present in many real problems from areas such as configuration and databases. As a result, numerous specialized algorithms that achieve generalized arc consistency (GAC) on table constraints have been proposed. Since these algorithms achieve GAC, they operate on one constraint at a time. In this paper we propose an efficient algorithm for table constraints that achieves a stronger local consistency than GAC. This algorithm, called maxRPWC+, is based on the local consistency maxRPWC and allows the efficient handling of intersecting table constraints. Experimental results from benchmark problems demonstrate that maxRPWC+ is clearly more robust than a state-of-the-art GAC algorithm in classes of problems with interleaved table constraints, being orders of magnitude faster in some of these classes.

Auto-pipeline

Recent work has made significant progress in helping users to automate single data preparation steps, such as string-transformations and table-manipulation operators (e.g., Join, GroupBy, Pivot, etc.). We in this work propose to automate multiple such steps end-to-end, by synthesizing complex data-pipelines with both string-transformations and table-manipulation operators. We propose a novel by-target paradigm that allows users to easily specify the desired pipeline, which is a significant departure from the traditional by-example paradigm. Using by-target, users would provide input tables (e.g., csv or json files), and point us to a "target table" (e.g., an existing database table or BI dashboard) to demonstrate how the output from the desired pipeline would schematically "look like". While the problem is seemingly under-specified, our unique insight is that implicit table constraints such as FDs and keys can be exploited to significantly constrain the space and make the problem tractable. We develop an AUTO-PIPELINE system that learns to synthesize pipelines using deep reinforcement-learning (DRL) and search. Experiments using a benchmark of 700 real pipelines crawled from GitHub and commercial vendors suggest that AUTO-PIPELINE can successfully synthesize around 70% of complex pipelines with up to 10 steps.

An approach to solution of constrained clustering problems using the constraint programming paradigm and the multiset theory

An integrated approach is proposed to solve the Constrained Clustering problems which are oriented on taking the opinion of a group of experts into account. A cluster and the objects to be clustered are proposed to be represented as multisets, and the distance between these to be determined by metrics in the Petrovsky multisets space. The approach is implemented within the Constraint Programming paradigm. In so doing, the significant complexity is in organizing effective processing the qualitative constraints, namely, the rules for assigning the objects to one or different clusters. The qualitative constraints are proposed to be represented and processed as table constraints of a new type, i.e., as the smart-tables of D-type. The main attention is confined to the problem of how to reduce the amount of constraints and how to simplify the Constrained Clustering problem. It is proposed to generate constraints for some pairs of objects rather than for all of them, with the generation based on a priori interval estimation of the optimal value of the clustering criterion. To do that, a modified method of multisets hierarchical clustering has been proposed. The approach proposed allows a global optimum to be found for the Constrained Clustering problems considered.

Интеграция методов поиска в ширину и логического вывода для удовлетворения табличных ограничений

Within the Constraint Programming technology, so-called table constraints such as typical tables, compressed tables, smart tables, segmented tables, etc, are widely used. They can be used to represent any other types of constraints, and algorithms of the table constraint propagation (logical inference on constraints) allow eliminating a lot of "redundant" values from the domains of variables, while having low computational complexity. In the previous studies, the author proposed to divide smart tables into structures of C- and D-types. The generally accepted methodology for solving constraint satisfaction problems is the combined application of constraint propagation methods and backtracking depth-first search methods. In the study, it is proposed to integrate breadth-first search methods and author`s method of table constraint propagation. D-type smart tables are proposed to be represented as a join of several orthogonalized C-type smart tables. The search step is to select a pair of C-type smart tables to be joined and then propagate the restrictions. To determine the order of joining orthogonalized smart tables at each step of the search, a specialized heuristic is used, which reduces the search space, taking into account further calculations. When the restrictions are extended, the acceleration of the computation process is achieved by applying the developed reduction rules for the case of C-type smart tables. The developed hybrid method allows one to find all solutions to the problems of satisfying constraints modeled using one or several D-type smart tables, without decomposing tabular constraints into elementary tuples.

Generalized Arc Consistency Algorithms for Table Constraints: A Summary of Algorithmic Ideas

Constraint Programming is a powerful paradigm to model and solve combinatorial problems. While there are many kinds of constraints, the table constraint (also called a CSP) is perhaps the most significant—being the most well-studied and has the ability to encode any other constraints defined on finite variables. Thus, designing efficient filtering algorithms on table constraints has attracted significant research efforts. In turn, there have been great improvements in efficiency over time with the evolution and development of AC and GAC algorithms. In this paper, we survey the existing filtering algorithms for table constraint focusing on historically important ideas and recent successful techniques shown to be effective.

Graphs with table constraints on reachability

On directed graphs defined a new kind of reachability restriction – table constraints on reachability. Each edge of the graph assigned a certain element of the monoid. Some element of the monoid selected and fixed. This element does not equal to the unit of the monoid. This element is called forbidden. Each way on the graph is associated with characteristic – a vector, whose length is equal to the number of way edges. First element of the characteristic is equal to the element of the monoid which corresponded to the first edge of the way. Each successive element of the characteristic is equal to the previous element of the characteristics plus the value of an element of the monoid, corresponding to the next edge of the way. A way on the graph is considered as valid if the way characteristic does not contain a forbidden element. The construction of the scan-graph, which is built on the original graph, is described. The transition to the scan-graph allows you to solve the problems of the reachability on such graphs, shortest ways and random walks on the graphs with table constraints on reachability.

Компактное представление ограничений на основе новой интерпретации понятия «кортеж многоместного отношения»

The article discusses various points of view on the concept of "tuple of a multi-place relation" used in mathematics and information technology. Special attention is paid to an evolution of the concept “tuple” within Constraint Programming technology where the emergence of new interpretations for the concept “tuple” is related with attempts to design more “compact” table representation of qualitative relations comparing with typical relational tables. This “compact” representation can serve as a basis for accelerating qualitative constraint satisfaction procedures. In studied prototype-works, such varieties of table constraints as compressed-tables and smart-tables were proposed. In so doing, the concept of compressed- and smart- tuple substantially differs from traditional concept of tuple of a multi-place relation. However, the known table constraints types are not well suited for modeling and processing all types of quality relations, for example, there are inconveniences when modeling production rules. The article proposes a new type of table constraints – smart-tables of D-type and equivalent transformations rules allowing the initial constraint satisfaction problem to be effectively reduced. The application of the smart-tables of D-type allows in some cases to substantially reduce computer memory consumption comparing with application of the known types of table constraints. In particular, smart-tables of D-types are well suited for modeling production rules, some types of logical expirations and some types of global constraints.

From MDD to BDD and Arc consistency

In this paper, we present a new conversion of multivalued decision diagrams (MDD) to binary decision diagrams (BDD) which can be used to improve MDD-based fil- tering algorithms such as MDDC or MDD-4R. We also propose BDDF, an algorithm that copies modified parts of the BDD “on the fly” during the search of a solution, and yields a better incrementality than a pure MDDC-like approach. MDDC is not very efficient when used to represent poorly structured positive table constraints. Our new representation combined with BDDF retains the properties of the MDD representation and has comparable performances to the STR2 algorithm by Ullmann (2007) and Lecoutre (Constraints, 16.4, 341–371 2011).

Encoding Domain Transitions for Constraint-Based Planning

We describe a constraint-based automated planner named Transition Constraints for Parallel Planning (TCPP). TCPP constructs its constraint model from a redefined version of the domain transition graphs (DTG) of a given planning problem. TCPP encodes state transitions in the redefined DTGs by using table constraints with cells containing don't cares or wild cards. TCPP uses Minion the constraint solver to solve the constraint model and returns a parallel plan. We empirically compare TCPP with the other state-of-the-art constraint-based parallel planner PaP2. PaP2 encodes action successions in the finite state automata (FSA) as table constraints with cells containing sets of values. PaP2 uses SICStus Prolog as its constraint solver. We also improve PaP2 by using don’t cares and mutex constraints. Our experiments on a number of standard classical planning benchmark domains demonstrate TCPP's efficiency over the original PaP2 running on SICStus Prolog and our reconstructed and enhanced versions of PaP2 running on Minion.

Extending Compact-Table to Negative and Short Tables

Table constraints are very useful for modeling combinatorial constrained problems, and thus play an important role in Constraint Programming (CP). During the last decade, many algorithms have been proposed for enforcing the property known as Generalized Arc Consistency (GAC) on such constraints. A state-of-the art GAC algorithm called Compact-Table (CT), which has been recently proposed, significantly outperforms all previously proposed algorithms. In this paper, we extend this algorithm in order to deal with both short supports and negative tables, i.e., tables that contain universal values and conflicts. Our experimental results show the interest of using this fast general algorithm.

Soft and Cost MDD Propagators

Recent developments of efficient propagators, operations and creation methods for MDDs allow us to directly build efficient MDD-based models, without the need for intermediate data structures. In this paper, we take another step in this direction by improving the propagators of cost MDDs. In addition, we introduce a soft MDD propagator in order to deal with unsatisfiable problems. This directly offers cost and soft versions for table constraints and any constraints which can be represented by an MDD (regular, slide, knapsack...).

A Constraint-Programmed Planner for Deep Space Exploration Problems With Table Constraints

In recent years because of the increasing number and types of scientific payloads on a probe, the constraints between payload and probe and the constraints among payloads have become increasingly complex. The technology of constraint processing has gradually become a focus of research in deep space planning. In this paper, we propose a constrained-programmed planner called DSPlan for deep space planning problems based on table constraints. We first propose a technique for automatically converting the planning domain definition language model used in planning into the form of table constraints. Following the common practice of coding a planning problem as a constraint satisfaction problem with multiple levels, we propose a dynamic constraint set and a corresponding mutex filtering algorithm to express the different combinations of constraints on varying levels that need to be satisfied. This new form of data structure uses explicit domain information to maintain the generalized arc consistency of table constraints. Empirical analyses demonstrate the efficiency of table constraints over the international planning competition problem and classic deep space instances in general arc consistency schema algorithms. Experimental results also prove that DSPlan and table constraints are highly promising general-purpose tools for deep space planning problems compared with other planners.