Algorithms — ESA 2001, 9th Annual European Symposium Århus, Denmark

Closest Vectors, Successive Minima, and Dual HKZ-Bases of Lattices - Blömer, Johannes (Automata, Languages and Programming)

Property Testing in Computational Geometry - Czumaj, Artur; Sohler, Christian; Ziegler, Martin (Proceedings of the 8th Annual European Symposium on Algorithms (ESA'00))
We consider the notion of Property Testing as applied to computational geometry. We aim at developing efficient algorithms which determine whether a given (geometrical) object has a predetermined property Q or is 'far' from any object having the property. We show that many basic geometric properties have very efficient testing algorithms, whose running time is significantly smaller than the object description size.

Medienbildung und Gesellschaft

Computing the Dimension of Linear Subspaces - Ziegler, Martin; Brattka, Vasco (SOFSEM 2000: Theory and Practice of Informatics)
Since its very beginning, linear algebra is a highly algorithmic subject. Let us just mention the famous Gauss Algorithm which was invented before the theory of algorithms has been developed. The purpose of this paper is to link linear algebra explicitly to computable analysis, that is the theory of computable real number functions. Especially, we will investigate in which sense the dimension of a given linear subspace can be computed. The answer highly depends on how the linear subspace is given: if it is given by a finite number of vectors whose linear span represents the space, then the dimension does not depend continuously on these vectors and consequently it cannot be computed. If the linear subspace is represented via its distance function, which is a standard way to represent closed subspaces in computable analysis, then the dimension does computably depend on the distance function.

Complexity Theory and Algorithms - Meyer auf der Heide, Friedhelm; Kutyłowski, Mirosław; Ragde, Prabhakar (Euro-Par 2000 Parallel Processing)

Large-Scale SCI Clusters in Practice: Architecture and Performance in SCI - Simon, Jens; Reinefeld, Alexander; Heinz, Oliver (SCI: Scalable Coherent Interface. Architecture and Software for High-Performance Compute Clusters)

Eine quasistationäre Meßmethode zur Ermittlung der Wärmeleitfähigkeit polymerer Zwischenschichten in Abhängigkeit von der Temperatur - Koyro, M.; Meschut, Gerson (Tagungsband zur Veranstaltung Werkstoffprüfung 1999)

New Results on Fault Tolerant Geometric Spanners - Lukovszki, Tamás (Proceedings of the 6th Workshop on Algorithms an Data Structures (WADS'99), LNCS)
We investigate the problem of constructing spanners for a given set of points that are tolerant for edge/vertex faults. Let S be a set of $n$ points in the d-dimensional space and let k be an integer number. A k-edge/vertex fault tolerant spanner for S has the property that after the deletion of k arbitrary edges/vertices each pair of points in the remaining graph is still connected by a short path. Recently it was shown that for each set S of n points there exists a k-edge/vertex fault tolerant spanner with O(k^2 n) edges which can be constructed in O(n log n + k^2 n) time. Furthermore, it was shown that for each set S of n points there exists a k-edge/vertex fault tolerant spanner whose degree is bouned by O(c^k+1) for some constant c. Our first contribution is a construction of a k-vertex fault tolerant spanner with O(kn) edges which is a tight bound. The computation takes O(n log^d-1 n + k n log log n) time. Then we show that the same k-vertex fault tolerant spanner is also k-edge fault tolerant. Thereafter, we construct a k-vertex fault tolerant spanner with O(k^2 n) edges whose degree is bounded by O(k^2). Finally, we give a more natural but stronger definition of k-edge fault tolerance which not necessarily can be satisfied if one allows only simple edges between the points of S. We investigate the question whether Steiner points help. We answer this question affirmatively and prove Theta(kn) bounds on the number of Steiner points and on the number of edges in such spanners.

Provably Good and Practical Strategies for Non-uniform Data Management in Networks - Meyer auf der Heide, Friedhelm; Vöcking, Berthold; Westermann, Matthias (Algorithms - ESA’ 99)

Communication Synthesis for Reconfigurable Embedded Systems - Eisenring, Michael; Platzner, Marco; Thiele, Lothar (Proceedings of the 9th International Workshop on Field Programmable Logic and Applications (FPL))

Geometric Searching in Walkthrough Animations with Weak Spanners in Real Time - Fischer, Matthias; Lukovszki, Tamás; Ziegler, Martin (Algorithms — ESA’ 98)
We study algorithmic aspects in the management of geometric scenes in interactive walkthrough animations. We consider arbitrarily large scenes consisting of unit size balls. For a smooth navigation in the scene we have to fulfill hard real time requirements. Therefore, we need algorithms whose running time is independent of the total number of objects in the scene and that use as small space as possible. In this work we focus on one of the basic operations in our walkthrough system: reporting the objects around the visitor within a certain distance. Previously a randomized data structure was presented that supports reporting the balls around the visitor in an output sensitive time and allows insertion and deletion of objects nearly as fast as searching. These results were achieved by exploiting the fact that the visitor moves ''slowly'' through the scene. A serious disadvantage of the aforementioned data structure is a big space overhead and the use of randomization. Our first result is a construction of weak spanners that leads to an improvement of the space requirement of the previously known data structures. Then we develop a deterministic data structure for the searching problem in which insertion of objects are allowed. Our incremental data structure supports O(1+k) reporting time, where k is a certain quantity close to the number of reported objects. The insertion time is similar to the reporting time and the space is linear to the total number of objects.

Communication-efficient parallel multiway and approximate minimum cut computation - Meyer auf der Heide, Friedhelm; Martinez, Gabriel Terán (LATIN'98: Theoretical Informatics)

Acceleration of satisfiability algorithms by reconfigurable hardware - Platzner, Marco; De Micheli, Giovanni (Proceedings of the 8th International Workshop on Field Programmable Logic and Applications (FPL))

Bounded degree spanning trees - Czumaj, Artur; Strothmann, Willy-Bernhard (Proceedings of the Fifth Annual European Symposium on Algorithms (ESA'97))
Given a connected graph $G$, let a $dT$-spanning tree of $G$ be a spanning tree of $G$ of maximum degree bounded by $dT$. It is well known that for each $dT ge 2$ the problem of deciding whether a connected graph has a $dT$-spanning tree is NP-complete. In this paper we investigate this problem when additionally connectivity and maximum degree of the graph are given. A complete characterization of this problem for 2- and 3-connected graphs, for planar graphs, and for $dT=2$ is provided. Our first result is that given a biconnected graph of maximum degree $2dT-2$, we can find its $dT$-spanning tree in time $O(m+n^3/2)$. For graphs of higher connectivity we design a polynomial-time algorithm that finds a $dT$-spanning tree in any $k$-connected graph of maximum degree $k(dT-2)+2$. On the other hand, we prove that deciding whether a $k$-connected graph of maximum degree $k(dT-2)+3$ has a $dT$-spanning tree is NP-complete, provided $k le 3$. For arbitrary $k ge 3$ we show that verifying whether a $k$-connected graph of maximum degree $k(dT-1)$ has a $dT$-spanning tree is NP-complete. In particular, we prove that the Hamiltonian path (cycle) problem is NP-complete for $k$-connected $k$-regular graphs, if $k>2$. This extends the well known result for $k=3$ and fully characterizes the case $dT=2$. For planar graphs it is NP-complete to decide whether a $k$-connected planar graph of maximum degree $dG$ has a $dT$-spanning tree for $k=1$ and $dG > dT ge 2$, for $k=2$ and $dG > 2(dT-1) ge 2$, and for $k=3$ and $dG > dT = 2$. On the other hand, we show how to find in polynomial (linear or almost linear) time a $dT$-spanning tree for all other parameters of $k$, $dG$, and $dT$.

Denesting by bounded degree radicals - Blömer, Johannes (Algorithms — ESA '97)

Dynamic data structures for realtime management of large geometric scenes - Fischer, Matthias; Meyer auf der Heide, Friedhelm; Strothmann, Willy-Bernhard (5th Annual European Symposium on Algorithms (ESA '97))
We present a data structure problem which describes the requirements of a simple variant of fully dynamic walk-through animation: We assume the scene to consist of unit size balls in R2 or higher dimensions. The scene may be arbitrarily large and has to be stored in secondary memory (discs) with relatively slow access. We allow a visitor to walk in the scene, and a modeler to update the scene by insertions and deletions of balls. We focus on the realtime requirement of animation systems: For some t (specified by the computation power of (the rendering hardware of) the graphic workstation) the data structure has to guarantee that the balls within distance t of the current visitor's position are presented to the rendering hardware, 20 times per second. Insertions and deletions should also be available to the visitor with small delay, independent of the size of the scene. We present a data structure that fulfills the above task in realtime. Its runtime is output-sensitive, i.e. linear in a quantity close to the output size of the query. We further present (preliminary) experimental results indicating that our structure is efficient in practice.

Static and dynamic data management in networks - Meyer auf der Heide, Friedhelm; Vöcking, Berthold (Euro-Par'97 Parallel Processing)

Communication efficient parallel searching - Bäumker, Armin; Meyer auf der Heide, Friedhelm (Solving Irregularly Structured Problems in Parallel)

Routing on asyncronous processor networks - Karaivazoglou, Efstratios; Meyer auf der Heide, Friedhelm (Euro-Par'97 Parallel Processing)