Bernd-Uwe Pagel

Towards an analysis of range query performance in spatial data structures

In this paper, we motivate four different user defined window query classes and derive a probabilistic model for each of them. For each model, we characterize the efficiency of spatial data structures in terms of the expected number of data bucket accesses needed to perform a window query. Our analytical approach exhibits the performance phenomena independent of data structure and implementation details and whether the objects are points or non-point objects.

GIS-application development with GEOOOA

We stress the need of a domain-tailored requirements engineering method for the development of GIS-applications. To this end, we discuss three GIS-application scenarios we have frequently encountered in real life projects. Our investigation reveals that conventional RE-methods like Coad/Yourdons Object-Oriented Analysis (OOA) are not capable of modelling GIS-specific requirements appropriately. To overcome the deficiencies of conventional OOA we introduce GEOOOA which extends OOA by domain-tailored primitives and allows for a more adequate treatment of GIS-specific requirements. We provide GEOOOA-models of three application scenarios which serve as first validation steps for the usefulness of the approach. Finally, we propose some methodological advices for a proper application of GEOOOA and sketch the GEOOOA-tool environment.

Window query-optimal clustering of spatial objects

During the last decade various spatial data structures have been designed and compared against each other with respect to their performance. Still missing is a lower bound result, e.g. an optimal spatial data clustering, which would allow for the absolute comparison of the performance of the well-known data structures with the optimum. In this paper, we address the static situation where the data is known in beforehand. An optimal data clustering for this setting will also provide a lower bound for the dynamic situation where the input data is not known in advance and the data structure is built up by iterated insertions. Using as performance measure the expected number of data bucket accesses needed to perform a window query, the static clustering problem turns into a classical optimization problem. For the special case of bucket capacity cb = 2 the optimization problem is solvable in polynomial time, whereas for cb 3 it is NP-hard. In experiments using simulated annealing heuristics for the optimization the best dynamic structures as well as the static packed R-tree perform about 20% worse than the optimum on average. However, we again want to emphazise that we understand our contribution as lower bound result rather than another speed-up variant of classical spatial data structures.

The Transformation Technique for Spatial Objects Revisited

The transformation technique is one of the earliest approaches for storing a set of bounding boxes of arbitrary geometric objects such that insertion, deletion and proximity queries can be carried out with reasonable performance. The basic idea is to transform the bounding boxes into points in higher dimensional space in order to apply data structures for points which are better understood and easier to handle. Even though the basic concept of the transformation idea at first glance seems fascinatingly simple and elegant, the majority of the data structure community regard this technique as less appropriate because some of its properties are considered harmful.

Are window queries representative for arbitrary range queries

In this paper, we characterize the eciency of spatial access structures in terms of the expected number of data bucket accesses needed to perform a range query. We derive performance formulas for various kinds of range queries like intersection, containment, and enclosure queries with dierent geometric shapes. The formulas exhibit that range query performance in general depends on three parameters: the area sum of the data regions, the perimeter sum, and the number of regions. Only the weights of these parameters vary from shape to shape and query type to query type. To a wide extent, our results prove the conjecture that window queries are representative for range queries in general.

The GeoOOA-tool and its interface to open software development environments for GIS

GEoOOA is an object-oriented requirements engineering method with suitable geo-primitives which allows an adequate treatment of GIS-specific requirements. Since the applicability and success of any software engineering method depends heavily on an appropriate tool support, we propose the GEOOOA-tool, a CASE-tool supporting the development of GEOOOA-models. In this paper, we report on the editors, browsers, validators, and documentation aids of the GEoOOA-tool and sketch its connection to common open software development environments for GIS as well as some prototyping issues. Major parts of the tool have already been implemented and are available via anonymous ftp.

Optimizing Spatial Data Structures For Static Data

During the last decade various spatial data structures have been designed and compared against each other, all of them reflecting a dynamic situation with ongoing object insertion and deletion processes. Assuming the frequently occurring situation where the data is known in beforehand and using as performance measure the expected number of data bucket accesses needed to perform a window query, the original dynamic clustering problem turns into a classical optimization problem. For the special case of bucket capacity c b = 2 we present a mapping onto the well-known graph matching problem. For the general case of c b ≥ 3 and arbitrary cost functions, the optimization problem is NP-hard. In first experiments with simulated annealing heuristics the best dynamic structures are outperformed by more than 25%. However, we understand our contribution as a lower bound result rather than another speed-up variant of classical spatial data structures.