Thomas Ottmann

The Authoring on the Fly system for automated recording and replay of (tele)presentations

Abstract. We discuss the problem of capturing media streams which occur during a live lecture in class or during a telepresentation. Instead of presenting yet another method or system for capturing the classroom experience, we introduce some informal guidelines and show their importance for such a system. We derive from these guidelines a formal framework for sets of data streams and an application model to handle these sets so that a real-time replay becomes possible. The Authoring on the Fly system is a possible realization of a framework which follows these guidelines. It allows the capture and real-time replay of data streams captured during a (tele)presentation, including audio, video, and whiteboard action streams. This article gives an overview of the different AoF system components for the various phases of the teaching and learning cycle. It comprises an integrated text and graphics editor for the preparation of pages to be loaded by the whiteboard during the presentation phase. The recording component of the system captures various data streams of the live presentation. They are postprocessed by the system so that they become instances of the class of media for whose replay the general application model was developed. From a global point of view, the Authoring on the Fly system allows one to merge three apparently distinct tasks – teaching in class, telepresentation, and multimedia authoring – into one single activity. The system has been used routinely for recording telepresentations over the MBone net and has already led to a large number of multimedia documents which have been integrated automatically into Web-based teaching and learning environments.

Numerical stability of geometric algorithms

This paper deals with the numerical problems involved in geometric computations. Our research wss very much motivated by a talk of A. R. Forrest at the 2nd ACM Symposium on Computational Geometry, Yorktown Heights, 1985, cf. [F]. There are only a very few papers in the open literature which adress the numerical problems in geometric computations. The textbooks mentioned above do not contain anything about the numerical problems in geometric computations. In an unpublished report [Ra] it is shown how to represent lines in the floating point system such that any two lines cannot intersect more than once. We refer to two papers which represent two extreme approaches in solving the numerical problems in geometric computations.

On the definition and computation of rectilinear convex hulls

Abstract Recently the computation of the rectilinear convex hull of a collection of rectilinear polygons has been studied by a number of authors. From these studies three distinct definitions of rectilinear convex hulls have emerged. We examine these three definitions for point sets in general, pointing out some of their consequences, and we give optimal algorithms to compute the corresponding rectilinear convex hulls of a finite set of points in the plane.

Dense multiway trees

B-trees of order <italic>m</italic> are a “balanced” class of <italic>m</italic>-ary trees, which have applications in the areas of file organization. In fact, they have been the only choice when balanced multiway trees are required. Although they have very simple insertion and deletion algorithms, their storage utilization, that is, the number of keys per page or node, is at worst 50 percent. In the present paper we investigate a new class of balanced <italic>m</italic>-ary trees, the dense multiway trees, and compare their storage utilization with that of B-trees of order <italic>m</italic>. Surprisingly, we are able to demonstrate that weakly dense multiway trees have an <italic>&Ogr;</italic>(log<subscrpt>2</subscrpt> <italic>N</italic>) insertion algorithm. We also show that inserting <italic>m<supscrpt>h</supscrpt></italic> - 1 keys in ascending order into an initially empty dense multiway tree yields the complete <italic>m</italic>-ary tree of height <italic>h</italic>, and that at intermediate steps in the insertion sequence the intermediate trees can also be considered to be as dense as possible. Furthermore, an analysis of the limiting dynamic behavior of the dense <italic>m</italic>-ary trees under insertion shows that the average storage utilization tends to 1; that is, the trees become as dense as possible. This motivates the use of the term “dense.”

New algorithms for special cases of the hidden line elimination problem

Hidden line elimination is a well-known problem in computer graphics and many practical solutions have been proposed. Only recently the problem has been studied from a theoretical point of view, taking asymptotic worst-case time- and spacebounds into account. Here we study three special cases of increasing difficulty and generality of the hidden line elimination problem. Applying some methods from computational geometry these problems can be solved with better worst-case bounds than those of the best known algorithms for the general problem.

Enumerating extreme points in higher dimensions

We consider the problem of enumerating all extreme points of a given set P of n points in d dimensions. We present a simple and practical algorithm which uses O(n) space and O(nm) time, where m is the number of extreme points of P. Our algorithm is designed to work even for highly degenerate input.We also present an algorithm to compute the depth of each point of the given set of n points in d-dimensions. This algorithm has time complexity O(n2) which significantly improves the O(n3) complexity of the naive algorithm.

The Complexity and Decidability of Separation

We study the difficulty of solving instances of a new family of sliding block puzzles called SEPARATIONTM. Each puzzle in the family consists of an arrangement in the plane of n rectilinear wooden blocks, n > 0. The aim is to discover a sequence of rectilinear moves which when carried out will separate each piece to infinity. If there is such a sequence of moves we say the puzzle or arrangement is separable and if each piece is moved only once we say it is one-separable. Furthermore if it is one-separable with all moves being in the same direction we say it is iso-separable.

Relaxed Balanced Red-Black Trees

Relaxed balancing means that, in a dictionary stored as a balanced tree, the necessary rebalancing after updates may be delayed. This is in contrast to strict balancing meaning that rebalancing is performed immediately after the update. Relaxed balancing is important for efficiency in highly dynamic applications where updates can occur in bursts. The rebalancing tasks can be performed gradually after all urgent updates, allowing the concurrent use of the dictionary even though the underlying tree structure is not completely in balance. In this paper we propose a new scheme of how to make known rebalancing techniques relaxed in an efficient way. The idea is applied to the red-black trees, but can be applied to any class of balanced trees. The key idea is to accumulate insertions and deletions such that they can be settled in arbitrary order using the same rebalancing operations as for standard balanced search trees. As a result it can be shown that the number of needed rebalancing operations known from the strict balancing scheme carry over to relaxed balancing.

On translating a set of line segments

Abstract An optimal one-pass algorithm is presented for the computation of an ordering for a set of line segments in the plane according to which the segments can be moved to the right by an arbitrary fixed distance, such that during the move no segment meets another.

Efficient labelling algorithms for the maximum noncrossing matching problem

Abstract Consider a bipartite graph; lets suppose we draw the origin nodes and the destination nodes arranged in two columns, and the edges as straight-line segments. A noncrossing matching is a subset of edges such that no two of them intersect. Several algorithms for the problem of finding the noncrossing matching of maximum cardinality are proposed. Moreover an extension to weighted graphs is considered.