Constraint programming is newly flowering in industry. Several companies have recently started up to exploit the technology, and the number of industrial applications is now growing very quickly. This survey will seek, by examples,

Strict consistency of replicated data is infeasible or not required by many distributed applications, so current systems often permit stale replication,inwhich cached copies of data values are allowed to become out of date. Queries over cached data return an answer quickly, but the stale answer may be unboundedly imprecise. Alternatively, queries over remote master data return a precise answer, but with potentially poor performance. To bridge the gap between these two extremes, we propose a new class of replication systems called TRAPP (Tradeoff in Replication Precision and Performance). TRAPP systems give each user fine-grained control over the tradeoff between precision and performance: Caches store ranges that are guaranteed to bound the current data values, instead of storing stale exact values. Users supply a quantitative precision constraint along with each query. To answer a query, TRAPP systems automatically select a combination of locally cached bounds and exact master data stored remotely to deliver a bounded answer consisting of a range that is no wider than the specified precision constraint, that is guaranteed to contain the precise answer, and that is computed as quickly as possible. This paper defines the architecture of TRAPP replication systems and covers some mechanics of caching data ranges. It then focuses on queries with aggregation, presenting optimization algorithms for answering queries with precision constraints, and reporting on performance experiments that demonstrate the fine-grained control of the precision-performance tradeoff offered by TRAPP systems.

. Constraint databases have recently been proposed as a powerful framework to model and retrieve spatial data. In a constraint database, a spatial object is represented as a quantifier free conjunction of (usually linear) constraints, called generalized tuple. The set of solutions of such quantifier free formula represents the set of points belonging to the extension of the object. The relational algebra can be easily extended to deal with generalized relations. However, such algebra has some limitations when it is used for modeling spatial data. First of all, there is no explicit way to deal with the set of points representing a spatial object as a whole. Rather, only point-based computations can be performed using this algebra. Second, practical constraint database languages typically use linear constraints. This allows to use efficient algorithms but, at the same time, some interesting queries cannot be represented (for example, the distance between two objects cannot be computed). ...

. Constraint databases generalize relational databases by finitely representable infinite relations. This paper surveys the state of the art in constraint databases: known results, remaining open problems and current research directions. The paper also describes a new algebra for databases with integer order constraints and a complexity analysis of evaluating queries in this algebra. In memory of Paris C. Kanellakis 1 Introduction There is a growing interest in recent years among database researchers in constraint databases, which are a generalization of relational databases by finitely representable infinite relations. Constraint databases are parametrized by the type of constraint domains and constraint used. The good news is that for many parameters constraint databases leave intact most of the fundamental assumptions of the relational database framework proposed by Codd. In particular, 1. Constraint databases can be queried by constraint query languages that (a) have a semantics ba...

Constraint relational databases use constraints to both model and query data. A constraint relation contains a finite set of generalized tuples. Each generalized tuple is represented by a conjunction of constraints on a given logical theory and, depending on the logical theory and the specific conjunction of constraints, it may possibly represent an infinite set of relational tuples. For their characteristics, constraint databases are well suited to model multidimensional and structured data, like spatial and temporal data. The definition of an algebra for constraint relational databases is important in order to make constraint databases a practical technology. In this paper, we extend the previously defined constraint algebra (called generalized relational algebra). First, we show that the relational model is not the only possible semantic reference model for constraint relational databases and we show how constraint relations can be interpreted under the nested relational model. Then...

. This paper describes the implementation of a constraint database system with integer and set of integers data types. The system called DISCO allows Datalog queries and input databases with both integer gap-order [30] and set order constraints [31]. The DISCO query language can easily express many complex problems involving sets. The paper also presents efficient running times for several sample queries. 1 Introduction Recently there has been much interest in constraint databases that generalize relational databases by allowing infinite relations that are finitely represented using constraint tuples (ex., [23, 3, 4, 8, 17, 21, 25, 28]). DISCO (short for Datalog with Integer and Set order COnstraints) is a constraint database system being developed at the University of Nebraska. DISCO implements a particular case of constraint query languages for which a general framework was proposed in [23] analogously to the constraint logic programming framework of Jaffar and Lassez [18]. The part...

. Aggregation queries are becoming increasingly common as databases continue to grow and provide parallel execution engines to enable complex queries over larger and larger amounts of data. Consequently, optimization of aggregation queries is becoming very important. In this paper we present a framework for reasoning with constraints arising from the use of aggregations. The framework introduces a constraint language, three types of inference rules to derive constraints that must hold given a set of aggregations and constraints in the query, and a sound and tractable inference procedure. The constraint language and inference procedure can be used by any system that deals with aggregations -- be it constraint programming, databases, or global information systems. However, the prime application of aggregation reasoning is in database query optimizers to optimize SQL (or object-SQL) queries with grouping and aggregation. Our framework allows aggregation reasoning to be incorporated into a...

Several authors have suggested to use first-order logic over the real numbers to describe spatial database applications. Geometric objects are then described by polynomial inequal-ities with integer coefficients involving the coordinates of the

: This paper presents MLPQ/GIS, a GIS database system that allows powerful and easy querying via a graphical user interface. The internal data representation of MLPQ/GIS is based on linear constraint databases, which can describe geo-spatiotemporal data, allow efficient conjunctive query evaluation, and facilitate data integration and database interoperability. 1 Introduction In the Millennium 2000, the World Wide Web will provide increased access to various types of databases all around the world. However, the incompatibility of different data models and formats used at different sites may hamper us in taking full advantage of the World Wide Web. It is, for example, difficult to integrate geographic data stored in an ARC/INFO GIS system [12] with temporal data stored in a TSQL temporal database system. Recently, Chomicki and Revesz [5] proposed to use constraint databases [10] as a common basis for various spatial, temporal and GIS data. The main motivation behind that proposal is th...

Abstract. It has been argued that the linear database model, in which semi-linear sets are the only geometric objects, is very suitable for most spatial database applications. For querying linear databases, the language FO + linear has been proposed. We present both negative and positive results regarding the expressiveness of FO+linear. First, weshow that the dimension query is de nable in FO + linear, which allows us to solve several interesting queries. Next, we show the non-de nability ofa whole class of queries that are related to sets not de nable in FO+linear. This result both sharpens and generalizes earlier results independently found by Afrati et al. and the present authors, and demonstrates the need for more expressive linear query languages if we want to sustain the desirability of the linear database model. In this paper, we showhow FO + linear can be strictly extended within FO + poly in a safe way. Whether any of the proposed extensions is complete for the linear queries de nable in FO + poly remains open. We doshow, however, that it is undecidable whether an expression in FO + poly induces a linear query. 1