A Mining-Based Compression Approach for Constraint Satisfaction Problems

In this paper, we propose an extension of our Mining for SAT framework to Constraint satisfaction Problem (CSP). We consider n-ary extensional constraints (table constraints). Our approach aims to reduce the size of the CSP by exploiting the structure of the constraints graph and of its associated microstructure. More precisely, we apply itemset mining techniques to search for closed frequent itemsets on these two representation. Using Tseitin extension, we rewrite the whole CSP to another compressed CSP equivalent with respect to satisfiability. Our approach contrast with previous proposed approach by Katsirelos and Walsh, as we do not change the structure of the constraints.Comment: arXiv admin note: substantial text overlap with arXiv:1304.441

STR2: Optimized Simple Tabular Reduction for Table Constraints

International audienceTable constraints play an important role within constraint programming. Recently, many schemes or algorithms have been proposed to propagate table constraints and/or to compress their representation. In this paper, we describe an optimization of simple tabular reduction (STR), a technique proposed by J. Ullmann to dynamically maintain the tables of supports when generalized arc consistency (GAC) is enforced/maintained. STR2, the new refined GAC algorithm we propose, allows us to limit the number of operations related to validity checking and search of supports. Interestingly enough, this optimization makes simple tabular reduction potentially r times faster where r is the arity of the constraint(s). The results of an extensive experimentation that we have conducted with respect to random and structured instances indicate that STR2 is usually around twice as fast as the original STR, two or three times faster than the approach based on the hidden variable encoding, and can be up to one order of magnitude faster than previously state-of-the art (generic) GAC algorithms on some series of instances. When comparing STR2 with the more recently developed algorithm based on multi-valued decision diagrams (MDDs), we show that both approaches are rather complementary

Generalized Hypertree Decomposition for solving non binary CSP with compressed table constraints

International audienc

STR et compression de contraintes tables

National audienceOver the recent years, many ltering algorithms have been developed for table constraints. STR2, one of the most e cient algorithms, is based on the technique of simple tabular reduction, meaning that it maintains dynamically the list of supports in each constraint table during inference and search. However, for some speci c problems, the approach that consists in representing in a compact way tables by means of multi-valued deci- sion diagrams (MDD) overcomes STR2. In this paper, we study the possibility of combining simple tabular reduction with a compression form of tables based on the detection of recurrent patterns in tuples

Domain value mutation and other techniques for constraint satisfaction problems

The term Constraint Satisfaction Problem (CSP) refers to a class of NP-complete problems, a collection of difficult problems for which no fast solution is known. The standard definition of a CSP involves variables, values, and constraints: each variable must be assigned a value from a designated group of possible values (also known as the variable’s domain), while a constraint on a set of variables indicates permissible combinations of values for these variables. Given a CSP, an important objective is to query whether it has a solution — an assignment of each variable to a value such that all constraints are satisfied. Solving a CSP usually requires chronological backtracking search that interleaves variable assignments with various kinds of inferences in order to reduce the search space. This dissertation comprises two parts. The first part deals with a modification of the classical CSP model that allows a value to be broken up and multiple values to be combined. The second part deals with generalized arc consistency algorithms. Both parts share a common theme in that extensional constraints --‐ the most basic expression possible for constraints --- play the central role. Despite being an important class, extensional constraints have received much less attention recently as most efforts have been channelled toward identifying new types of specialized constraints and coming up with corresponding algorithms. Regardless, improvements to algorithms for extensional constraints are more fundamental. This dissertation will attempt to improve existing techniques and algorithms for extensional constraints by examining them critically from the bottom up and approaching them from a novel direction

Further empowering variant tables for mass customization

Tables are a standard form of data representation in business. A variant table lists valid or excluded combi-nations of product features where each table column refers to a product property and each table row denotes a combination of product features. A table cell defines a feature, e.g. Color = Red, as an assignment of its value to the column's property. As technology and consumer demand drive ever increasing product choices, the number of feature combinations that can be offered for a product increases exponentially and can easily exceed the limits of a traditional table. However, variant tables can often be compressed in a way that scales both in size and query performance while retaining the tabular paradigm in a manner useful for a business. The basic idea is to partition the table rows into unconstrained slices, where each slice consists of all possible combinations of the product features it references. Such a slice can be represented as a c-tuple and readily stored in a spreadsheet. C-tuple representation is already supported in some product configurators. We give examples of products where it is feasible to efficiently represent all valid variants in one overall table using c-tuple compression. For cases where c-tuples do not suffice, the stronger compression to a variant decom-position diagram (VDD), a form of decision diagram, can be used. We propose complexity measures for a product based on the compressibility of its variants and discuss their usefulness to the business. We illustrate these ideas with examples and present some results on dealing with variant tables from real-world product models. We show that compression empowers variant tables by enabling enormous tables to be functionally used in a way like regular tables

Designing and Optimizing Representations for Non-Binary Constraints

Ph.DDOCTOR OF PHILOSOPH

The Effect of Representations on Constraint Satisfaction Problems

Constraint Satisfaction is used in the solution of a wide variety of important problems such as frequency assignment, code analysis, and scheduling. It is apparent that the modelling process is key to the success of any constraint based technique, and much work has been done on the identification of good models [FJHM05]. One of the key choices made during the modelling process is the selection of a constraint representation with which to express the constraints [HS02]. Whilst practitioners will commonly use an implicit representation, most existing structural tractability results are defined for explicit representation. We address a well-known anomaly in structural tractability theory, that acyclic instances are tractable when expressed explicitly, but may not be when expressed implicitly, and show that there is a link between representation and tractability, We introduce the notion of interaction width in order to address this disconnect between theory and practice, and use this to define new tractable classes by applying existing structural tractability results to different constraint representations, We show that for a given succinct representation, a non-trivial class of instances with bounded interaction width can be transformed into an explicit representation in polynomial time 50 that existing structural tractability results may be applied, We compare our work to existing results Cor alternative succinct representutions and show that the tractable classes we have defined arc incomparable and novel, and can be used to deduce new tractable classes for SAT. 3EThOS - Electronic Theses Online ServiceGBUnited Kingdo