Two different techniques of browsing through a collection of spatial objects stored in an R-tree spatial data structure on the basis of their distances from an arbitrary spatial query object are compared. The conventional approach is one that makes use of a k-nearest neighbor algorithm where k is known prior to the invocation of the algorithm. Thus if m#kneighbors are needed, the k-nearest neighbor algorithm needs to be reinvoked for m neighbors, thereby possibly performing some redundant computations. The second approach is incremental in the sense that having obtained the k nearest neighbors, the k +1 st neighbor can be obtained without having to calculate the k +1nearest neighbors from scratch. The incremental approach finds use when processing complex queries where one of the conditions involves spatial proximity (e.g., the nearest city to Chicago with population greater than a million), in which case a query engine can make use of a pipelined strategy. A general incremental nearest neighbor algorithm is presented that is applicable to a large class of hierarchical spatial data structures. This algorithm is adapted to the R-tree and its performance is compared to an existing k-nearest neighbor algorithm for R-trees [45]. Experiments show that the incremental nearest neighbor algorithm significantly outperforms the k-nearest neighbor algorithm for distance browsing queries in a spatial database that uses the R-tree as a spatial index. Moreover, the incremental nearest neighbor algorithm also usually outperforms the k-nearest neighbor algorithm when applied to the k-nearest neighbor problem for the R-tree, although the improvement is not nearly as large as for distance browsing queries. In fact, we prove informally that, at any step in its execution, the incremental...

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In this paper, we consider the filter step of the spatial join problem, for the case where neither of the inputs are indexed. We present a new algorithm, Scalable Sweeping-Based Spatial Join (SSSJ), that achieves both efficiency on real-life data and robustness against highly skewed and worst-case data sets. The algorithm combines a method with theoretically optimal bounds on I/O transfers based on the recently proposed distribution-sweeping technique with a highly optimized implementation of internal-memory plane-sweeping. We present experimental results based on an efficient implementation of the SSSJ algorithm, and compare it to the state-ofthe-art Partition-Based Spatial-Merge (PBSM) algorithm of Pate1 and DeWitt.

The declarativeness of relational query languages is very attractive for developing applications. However, many applications also need to invoke external functions or to access data that is not stored in the database. It is not hard to express references to such foreign functions in the query language. However, the issue of cost-based optimization of relational queries in the presence of such foreign functions has not previously been addressed satisfactorily. In this paper, we describe a comprehensive approach to this problem. Our key observation is that the optimization must take into account semantic information about foreign functions. Therefore, we provide a simple declarative rule language to express such semantics. We present algorithms necessary for applying the rules and for generating the space of equivalent queries. The equivalent queries provide the optimizer with an enriched execution space. We show how we can modify the traditional join reordering algorithm based on dynami...

Spatial data types or algebras for database systems should (1) be fully general, that is, closed under set operations, (2) have formally defined semantics, (3) be defined in terms of finite representations available in computers, (4) offer facilities to enforce geometric consistency of related spatial objects, and (5) be in-dependent of a particular DBMS data model, but cooperate with any. We present an algebra that uses realms as geometric domains underlying spatial data types. A realm, as a general database concept, is a finite, dynamic, user-defined structure underlying one or more system data types. Problems of numerical robustness and topological correctness are solved within and below the realm layer so that spatial algebras defined above a realm have very nice algebraic properties. Realms also interact with a DMBS to enforce geometric consistency on object creation or up-date. The ROSE algebra is defined on top of realms and offers general types to represent point, line, and region features, together with a comprehensive set of operations. It is described within a polymorphic type system and interacts with a DMBS data model and query language through an abstract object model interface. An example integration of ROSE into the object-oriented data model 02 and its query language is presented.

We propose a data model and query language that integrates an explicit modeling and querying of graphs smoothly into a standard database environment. For standard applications, some key features of object-oriented modeling are offered such as object classes organized into a hierarchy, object identity, and attributes referencing objects. Querying can be done in a familiar style with a derive statement that can be used like a select... from... where. On the other hand, the model allows for an explicit representation of graphs by partitioning object classes into simple classes, link classes, and path classes whose objects can be viewed as nodes, edges, and explicitly stored paths of a graph (which is the whole database instance). For querying graphs, the derive statement has an extended meaning in that it allows one to refer to subgraphs of the database graph. A powerful rewrite operation is offered for the manipulation of heterogeneous sequences of objects which often occur as a result of accessing the database graph. Additionally there are special graph operations like determining a shortest path or a subgraph and the model is extensible by such operations. Besides being attractive for standard applications, the model permits a natural representation and sophisticated querying of networks, in particular of spatially embedded networks like highways, public transport, etc.

Abstract: The ROSE algebra, defined earlier, is a system of spatial data types for use in spatial database systems. It offers data types to represent points, lines, and regions in the plane together with a comprehensive set of operations; semantics of types and operations have been formally defined. Values of these data types have a quite general structure, e.g. an object of type regions may consist of several polygons with holes. All ROSE objects are realm-based which means all points and vertices of objects lie on an integer grid and no two distinct line segments of any two objects intersect in their interior. In this paper we describe the implementation of the ROSE algebra, providing data structures for the types and new realm-based geometric algorithms for the operations. The main techniques used are (parallel) traversal of objects, plane-sweep, and graph algorithms. All algorithms are analyzed with respect to their worst case time and space requirements. Due to the realm properties, these algorithms are relatively simple, efficient, and numerically completely robust. All data structures and algorithms have indeed been implemented in the ROSE system; the Modula-2 source code is freely available from the authors for study or use.

In this work, we propose and assess a technique called bypass processing for optimizing the evaluation of disjunctive queries with expensive predicates. The technique is particularly useful for optimizing selection predicates that contain terms whose evaluation costs vary tremendously; e.g., the evaluation of a nested subquery or the invocation of a user-defined function in an object-oriented or extended relational model may be orders of magnitude more expensive than an attribute access (and comparison). The idea of bypass processing consists of avoiding the evaluation of such expensive terms whenever the outcome of the entire selection predicate can already be induced by testing other, less expensive terms. In order to validate the viability of bypass evaluation, we extend a previously developed optimizer architecture and incorporate three alternative optimization algorithms for generating bypass processing plans. 1 Introduction During the past few years we have witnessed tremendous...

Adopting the blackboard architecture from the area of Artificial Intelligence, a novel kind of optimizer enabling two desirable ideas will be proposed. Firstly, using such a well-structured approach backpropagation of the optimized queries allows an evolutionary improvement of (crucial) parts of the optimizer. Secondly, the A 3 search strategy can be applied to harmonize two contrary properties: Alternatives are generated whenever necessary, and straight-forward optimizing is performed whenever possible, however. The generic framework for realizing a blackboard optimizer is proposed first. Then, in order to demonstrate the viability of the new approach, a simple example optimizer is presented. It can be viewed as an incarnation of the generic framework. 1 Introduction Query optimizers---no matter whether relational or object-oriented---are among the most complex software systems that have been built. Therefore, it is not surprising that the design of query optimizers is still a "hot...

We propose a framework for the specification of extensible database systems. A particular goal is to implement a software component for parsing and rule-based optimization that can be used with widely varying data models and query languages as well as representation and query processing systems. The key idea is to use second-order signature (and algebra), a system of two coupled many-sorted signatures, where the top-level signature offers kinds and type constructors and the bottom-level signature provides polymorphic operations over the types defined as terms of the top level. Hence the top level can be used to define a data or representation model and the bottom level to describe a query algebra or a query processing algebra. We show the applicability of this framework by examples drawn from relational modeling and query processing.