Hans-Werner Six

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.

The R-file: an efficient access structure for proximity queries

In many nonstandard database applications, spatial access to geometric objects is very important. A new access structure, the R-file, is presented for geometric objects in a dynamic environment. An extensive performance evaluation reveals that the R-file, which is based on handling axis-parallel rectangles in secondary storage, has higher storage space utilization and a more compact directory, and turns out to be more efficient in exact match and window queries than comparable schemes, e.g. R-trees or grid file variants, for example, for maintaining geometric objects.<<ETX>>

The rectangle intersection problem revisited

We take another look at the problem of intersecting rectangles with parallel sides. For this we derive a one-pass, time optimal algorithm which is easy to program, generalizes tod dimensions well, and illustrates a basic duality in its data structures and approach.

On the correspondence between AVL trees and brother trees

We discuss the relationships of the classes of height-balanced (search) trees and the classes of brother (search) trees. In particular we characterize each class of height-balanced trees in terms of the class of “corresponding” brother trees and vice versa. Secondly, we show how this characterization leads to the notion of nonstandard updating algorithms. We derive a nonstandard insertion algorithm for height-balanced search trees to illustrate the notion. Finally we consider something of the similarities and differences between the standard and nonstandard insertion algorithms for height-balanced search rees.ZusammenfassungWir diskutieren die Beziehungen zwischen der Klasse der höhenbalanzierten (Such-) Bäume und der Klasse der Bruder-(Such-) Bäume. Insbesondere wird jede Klasse höhenbalanzierter Bäume durch die Klasse “entsprechender” Bruder-Bäume charakterisiert und umgekehrt. Zweitens zeigen wir, wie diese Charakterisierung zu nichtstandard Rebalanzierungs-Algorithmen führt. Wir erläutern dies am Beispiel des Einfüge-Algorithmus für höhenbalanzierte Bäume. Abschließend gehen wir auf einige Ähnlichkeiten und Unterschiede zwischen standard- und nichtstandard Einfüge-Algorithmen für höhenbalanzierte Bäume ein.

Right brother trees

Insertion and deletion algorithms are provided for the class of right (or one-sided) brother trees which have O (log n) performance. The importance of these results stems from the close relationship of right brother trees to one-sided height-balanced trees which have an insertion algorithm operating in O (log2 n). Further, although both insertion and deletion can be carried out in O (log n) time for right brother trees, it appears that the insertion algorithm is inherently much more difficult than the deletion algorithm—the reverse of what one usually obtains.

Spatial Access Structures for Geometric Databases

This paper surveys basic concepts of spatial access structures for geometric databases. We discuss the isolated plausibility arguments on which spatial access structure design decisions are traditionally based whenever efficiency is the primary goal, and we propose a more integrated view. This helps to explain phenomena that have been observed in experiments, and it lays the foundation for tailoring spatial access structures to the particular application requirements.

On the analysis of grid structures for spatial objects of non-zero size

We analyze the multilayer paradigm, a general principle for transforming index structures for points into index structures for non-zero size objects. For a specific multilayer grid structure, we perform a worst case analysis. A first step towards an average case analysis of grid structures is presented, where random intervals in a randomly divided data space are investigated.

Binary search trees with binary comparison cost

We introduce a new variant of the cost measure usually associated with binary search trees. This cost measure BCOST, results from the observation that during a search, a decision to branch left need require only one binary comparison, whereas branching right or not branching at all requires two binary comparisons. This is in contrast with the standard cost measure TCOST, which assumes an equal number of comparisons is required for each of the three possible actions. With BCOST in mind we re-examine its effect with respect to minimal and maximal BCOST trees, minimal and maximal BCOST-height trees, and introduce a class of BCOST-height balanced trees, which have a logarithmically maintainable stratified subclass. Finally, a number of other issues are briefly touched upon.

One-sided k-height-balanced trees

The purpose of this paper is to generalize the recent results on one-sided height-balanced trees (OSHB trees) to the case of one-sidedk-height-balanced trees, fork≥2. Surprisingly, this generalization leads to 0 (log2n) insertion and deletion algorithms, which are simpler than those available for OSHB trees, and thus we claim this generalization is of independent interest.ZusammenfassungIn dieser Arbeit werden die kürzlich erzielten Resultate über einseitig höhenbalanzierte Bäume (OSHB-Bäume) verallgemeinert auf den Fall einseitigk-höhenbalanzierter Bäume fürk≥2. Überraschenderweise führt die Verallgemeinerung zu 0(log2n) Einfüge- und Entferne-Algorithmen, die einfacher sind als die entsprechenden Algorithmen für OSHB-Bäume. Wir glauben daher, daß diese Verallgemeinerung an sich interessant ist.

A Framework for Data Structures

In this paper we outline a framework for data structures in the spirit of the Vienna Definition Language but extended to the most general class of objects, namely arbitrary directed rooted graphs in which the information associated with each node is either empty, elementary or an object in the general class. Since many data structures cannot be modelled by tree structures in a natural way, such a generalisation to graphs is desirable. Furthermore, the concept of hierarchy in which a node may serve for an arbitrary complex substructure supports a structured view of complex data objects.