Optimal broadcast on parallel locality models - Juurlink, Bernhardus; Kolman, Petr; Meyer auf der Heide, Friedhelm; Rieping, Ingo (Journal of Discrete Algorithms)

Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures - SPAA '03

A holistic methodology for network processor design - Bonorden, Olaf; Bruls, N.; Kastens, U.; Le, D. K.; Meyer auf der Heide, Friedhelm; Niemann, J.-C.; Porrmann, M.; Rückert, U.; Slowik, A.; Thies, M. (28th Annual IEEE International Conference on Local Computer Networks)

Composition of Efficient Nested BSP Algorithms: Minimum Spanning Tree Computation as an Instructive Example - Bonorden, Olaf; Meyer auf der Heide, Friedhelm; Wanka, Rolf (Int. Conf. on Parallel and Distributed Processing Techniques and Applications (PDPTA))

Any Load-Balancing Regimen for Evolving Tree Computations on Circulant Graphs Is Asymptotically Optimal - Wanka, Rolf (Proc. Workshop on Graph-Theoretic Concepts in Computer Science (WG))

Realtime Navigation in Highly Complex 3D-Scenes Using JPEG Compression - Klein, Jan; Krokowski, Jens; Cuntz, Nicolas (Proc. of 4. GI-Informatiktage)
We present a new and easy to use framework for navigating through scenes of arbitrary complexity and topology. In the preprocessing, images for discrete viewpoints and viewing directions are rendered and stored on an external volume. During navigation each image can be displayed within a very short time by loading it from the volume. For acceleration, our prefetching strategy loads possibly needed images for the next few frames if the viewer takes a break. The measurements show that we achieve interactive frame rates, whereby the difference between the minimal and maximal display time is very small. Our system works well with scenes modelled by polygons, but also digital photos can easily be used for describing a 3D scene.

Formal Description of a Distributed Location Service for Mobile Ad Hoc Networks - Benczúr, András; Glässer, Uwe; Lukovszki, Tamás (Proc. of 10th International Workshop on Abstract State Machines, LNCS)
We define here a distributed abstract state machine (DASM) [7] of the network or routing layer of mobile ad hoc networks [13]. Such networks re- quire routing strategies substantially different from those used in static commu- nication networks, since storing and updating large routing tables at mobile hosts would congest the network with administration packets very fast. In [1], the hypercubic location service is presented, which considers a very strong definition of fault-tolerance thereby improving state-of-the-art ad hoc routing protocols in several respects. Our goal in modeling the protocols for the distrib- uted location service and the position based routing is twofold. First, we support the definition and validation of wireless communication protocols and imple- mentations based thereon. Second, we feel that the abstract computation model naturally reflects the layering principle of communication architectures in com- bination with an uncompromisingly local view of the application domain. Thus we can identify fundamental semantic concepts, such as concurrency, reactivity and asynchronism, directly with the related concepts as imposed by the given application context.

Distributed Maintenance of Resource Efficient Wireless Network Topologies - Grünewald, Matthias; Lukovszki, Tamás; Schindelhauer, Christian; Volbert, Klaus (Proceedings of the 8th International Euro-Par Conference)

A simulation environment for ad hoc networks using sector subdivision - Volbert, Klaus (Proceedings 10th Euromicro Workshop on Parallel, Distributed and Network-based Processing)

Compact, adaptive placement schemes for non-uniform requirements - Brinkmann, André; Salzwedel, Kay; Scheideler, Christian (SPAA)

Abstract Combinatorial Programs and Efficient Property Testers - Sohler, Christian; Czumaj, Artur (Proceedings of the 43th Symposium on Foundations of Computer Science (FOCS))

A Degree O(log log n) Fault Tolerant Distributed Location Service for Geographic Ad-Hoc Routing - Lukovszki, Tamás; Benczúr, A.

Zur Berechenbarkeit reeller geometrischer Probleme - Ziegler, Martin
Die Implementierung von Algorithmen zur Lösung geometrischer Probleme im Euklidischen Raum (z.B. Berechnung der konvexen Hülle oder des Durchschnitts zweier Polyeder) stellt sich oftmals als hochgradig nichttrivial heraus. Ob und unter welchen Voraussetzungen die verursachenden numerischen Instabilitäten überhaupt ini den Griff zu kriegen oder vielmehr dem Problem inhärent sind, untersucht diese Arbeit in einem auf Turing zurückgehenden Rechenmodell. Im Gegensatz zu algebraischen Ansätzen geht jenes nicht von der Verfügbarkeit exakter Tests auf z.B. Gleichheit reeller Zahlen aus, sondern berücksichtigt die auf Digitalcomputern tatsächlich realisierbare Approximation durch rationale Zahlen. In diesem Rahmen werden beweisbar stabile Algorithmen zum Lösen linearer Gleichungssysteme, zur Matrix-Diagonalisierung und zur linearen wie nichtlinearen Optimierung präsentiert. Als wichtiges technisches Hilfsmittel dient ein neuer Berechenbarkeitsbegriff für reguläre unendliche Mengen reller Zahlen, der sich aus dem systematischen Vergleich verschiedener der Literatur entnommener ad-hoc Ansätze ergibt.

Computability on Regular Subsets of Euclidean Space - Ziegler, Martin (Mathematical Logic Quarterly (MLQ))

Point Location Algorithms of Minimum Size - Ziegler, Martin; Damerow, Valentina; Finschi, Lukas (Proceedings of the 14th Canadian Conference on Computational Geometry (CCCG'02))
Consider the classical point location problem: for a fixed arrangement of m hyperplanes and its induced partition of d-space report, upon input of some point, which face it lies in. With sufficient memory, this is easy to solve in logarithmic time O(log m). But how fast can algorithms (formalized as Linear Decision Trees) of *minimum* size be? The present work gives lower and upper bounds for the time complexity of point location under this constraint. They show that, in addition to m, the maximum number w of walls of a cell turns out to be a crucial parameter. We also consider a relaxation of the strict minimum-size condition allowing for constant factor overhead.

Computability of Linear Equations - Brattka, Vasco; Ziegler, Martin (Proceedings of the 2nd IFIP International Conference on Theoretical Computer Science)
Do the solutions of linear equations depend computably on their coefficients? Implicitly, this has been one of the central questions in linear algebra since the very beginning of the subject and the famous Gauß algorithm is one of its numerical answers. Today there exists a tremendous number of algorithms which solve this problem for different types of linear equations. However, actual implementations in floating point arithmetic keep exhibiting numerical instabilities for ill-conditioned inputs. This situation raises the question which of these instabilities are intrinsic, thus caused by the very nature of the problem, and which are just side effects of specific algorithms. To approach this principle question we revisit linear equations from the rigorous point of view of computability. Therefore we apply methods of computable analysis, which is the Turing machine based theory of computable real number functions. It turns out that, given the coefficients of a system of linear equations, we can compute the space of solutions, if and only if the dimension of the solution space is known in advance. Especially, this explains why there cannot exist any stable algorithms under weaker assumptions.

Bi-directional Coupling of Simulation Tools with a Walkthrough-System - Mueck, Bengt; Dangelmaier, Wilhelm; Fischer, Matthias; Klemisch, Wolfram (Simulation und Visualisierung)
Visualising is a method used to help experiencing and understanding causal cohesions in simulation processes. For this purpose, tools for visualising are already implemented in prevalent simulation systems. The user creates his simulation model and generates a 3-dimensional (2,5-dimensional) visualising by means of the simulation system. This helps examining the process which makes it easier for the viewer to understand it. Simulation tools usually only provide the opportunity for a unidirectional visualising. In a 3-dimensional surrounding the viewer can not implement an interaction with the simulation while the system is running. Though an interaction during the simulation run enables the user to gain a better understanding of causal cohesions. Solutions via HLA are sophisticated and therefore rather suited for extensive projects. We present a distributed system consisting of a commercial manufacturing simulation tool, a coupling module and a walkthrough system. The distributed system in conjunctions with the coupling module guarantees generality and a wide field of applications of the walkthrough system. Further it guarantees flexibility and selection of the specialized graphics hardware for the walkthrough system. A further contribution of this paper is the solution of the time synchronisation problem caused by simulation tool and walkthrough system.

Randomized Pursuit-Evasion in Graphs - Adler, Micah; Räcke, Harald; Sivadasan, Naveen; Sohler, Christian; Vöcking, Berthold (Proceedings of the 29th International Colloquium on Automata, Languages and Programming)
We analyze a randomized pursuit-evasion game on graphs. This game is played by two players, a hunter and a rabbit. Let G be any connected, undirected graph with n nodes. The game is played in rounds and in each round both the hunter and the rabbit are located at a node of the graph. Between rounds both the hunter and the rabbit can stay at the current node or move to another node. The hunter is assumed to be restricted to the graph G: in every round, the hunter can move using at most one edge. For the rabbit we investigate two models: in one model the rabbit is restricted to the same graph as the hunter, and in the other model the rabbit is unrestricted, i.e., it can jump to an arbitrary node in every round. We say that the rabbit is caught as soon as hunter and rabbit are located at the same node in a round. The goal of the hunter is to catch the rabbit in as few rounds as possible, whereas the rabbit aims to maximize the number of rounds until it is caught. Given a randomized hunter strategy for G, the escape length for that strategy is the worst case expected number of rounds it takes the hunter to catch the rabbit, where the worst case is with regards to all (possibly randomized) rabbit strategies. Our main result is a hunter strategy for general graphs with an escape length of only O (n log (diam(G))) against restricted as well as unrestricted rabbits. This bound is close to optimal since Ω(n) is a trivial lower bound on the escape length in both models. Furthermore, we prove that our upper bound is optimal up to constant factors against unrestricted rabbits.

Data Management in Networks: Experimental Evaluation of a Provably Good Strategy - Krick, Christof; Meyer auf der Heide, Friedhelm; Räcke, Harald; Vöcking, Bernhard; Westermann, Matthias' (Theory of Computing Systems)

The randomized sample tree: a data structure for interactive walkthroughs in externally stored virtual environments - Klein, Jan; Krokowski, Jens; Fischer, Matthias; Wand, Michael; Wanka, Rolf; Meyer auf der Heide, Friedhelm (Proceedings of the ACM symposium on Virtual reality software and technology - VRST '02)
We present a new data structure for rendering highly complex virtual environments of arbitrary topology. The special feature of our approach is that it allows an interactive navigation in very large scenes (30 GB/400 million polygons in our benchmark scenes) that cannot be stored in main memory, but only on a local or remote hard disk. Furthermore, it allows interactive rendering of substantially more complex scenes by instantiating objects. For the computation of an approximate image of the scene, a sampling technique is used. In the preprocessing, a so-called sample tree is built whose nodes contain randomly selected polygons from the scene. This tree only uses space that is linear in the number of polygons. In order to produce an image of the scene, the tree is traversed and polygons stored in the visited nodes are rendered. During the interactive walkthrough, parts of the sample tree are loaded from local or remote hard disk. We implemented our algorithm in a prototypical walkthrough system. Analysis and experiments show that the quality of our images is comparable to images computed by the conventional z-buffer algorithm regardless of the scene topology.

Energy, congestion and dilation in radio networks - Meyer auf der Heide, Friedhelm; Schindelhauer, Christian; Volbert, Klaus; Grünewald, Matthias (Proceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures - SPAA '02)

Mobile Computing, Mobile Networks - Meyer auf der Heide, Friedhelm; Kumar, Mohan; Nikoletseas, Sotiris; Spirakis, Paul (Euro-Par 2002 Parallel Processing)

Balls into Bins: A Paradigm for Job Allocation, Data Distribution Processes, and Routing - Schröder, Klaus

Efficient Parallel Simulations of Pulse-Coded Neural Networks (PCNN) - Salzwedel, Kay; Hartmann, Georg; Wolff, Carsten; Preis, Robert (Proceedings of the PDPTA 2001)

Deterministic Routing With Bounded Buffers: Turning Offline Into Online Protocols - Meyer auf der Heide, Friedhelm; Scheideler, Christian (Combinatorica)

SIMLAB-A Simulation Environment for Storage Area Networks - Berenbrink, Petra; Brinkmann, André; Scheideler, Christian (PDP)

Testing Hypergraph Coloring - Czumaj, Artur; Sohler, Christian (Proceedings of the 28th International Colloquium on Automata, Languages and Programming (ICALP))

Soft Kinetic Data Structures - Sohler, Christian; Czumaj, Artur (Proceedings of the 12th ACM-SIAM Symposium on Discrete Algorithms)

Property Testing with Geometric Queries - Sohler, Christian; Czumaj, Artur (Proceedings of the 9th Annual European Symposium on Algorithms (ESA`01))
This paper investigates geometric problems in the context of property testing algorithms. Property testing is an emerging area in computer science in which one is aiming at verifying whether a given object has a predetermined property or is “far” from any object having the property. Although there has been some research previously done in testing geometric properties, prior works have been mostly dealing with the study of combinatorial notion of the distance defining whether an object is “far” or it is “close”; very little research has been done for geometric notion of distance measures, that is, distance measures that are based on the geometry underlying input objects. The main objective of this work is to develop sound models to study geometric problems in the context of property testing. Comparing to the previous work in property testing, there are two novel aspects developed in this paper: geometric measures of being close to an object having the predetermined property, and the use of geometric data structures as basic primitives to design the testers. We believe that the second aspect is of special importance in the context of property testing and that the use of specialized data structures as basic primitives in the testers can be applied to other important problems in this area. We shall discuss a number of models that in our opinion fit best geometric problems and apply them to study geometric properties for three very fundamental and representative problems in the area: testing convex position, testing map labeling, and testing clusterability.

I/O-Efficient Batched Range Counting and Its Applications to Proximity Problems - Lukovszki, Tamás; Maheshwari, Anil; Zeh, Norbert (Proceedings of the 21st Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2001), LNCS)

Factoring a binary polynomial of degree over one million - Bonorden, Olaf; von zur Gathen, Joachim; Gerhard, Jürgen; Müller, Olaf (ACM SIGSAM Bulletin)
On 22 May 2000, the factorization of a pseudorandom polynomial of degree 1 048 543 over the binary field Z 2 was completed on a 4-processor Linux PC, using roughly 100 CPU-hours. The basic approach is a combination of the factorization software BIPOLAR and a parallel version of Cantor's multiplication algorithm. The PUB-library (Paderborn University BSP library) is used for the implementation of the parallel communication.

A Computable Spectral Theorem - Ziegler, Martin; Brattka, Vasco (Proceedings of the 4th Workshop on Computability and Complexity in Analysis (CCA'2000))
Computing the spectral decomposition of a normal matrix is among the most frequent tasks to numerical mathematics. A vast range of methods are employed to do so, but all of them suffer from instabilities when applied to degenerate matrices, i.e., those having multiple eigenvalues. We investigate the spectral representation's effectivity properties on the sound formal basis of computable analysis. It turns out that in general the eigenvectors cannot be computed from a given matrix. If however the size of the matrix' spectrum (=number of different eigenvalues) is known in advance, it can be diagonalized effectively. Thus, in principle the spectral decomposition can be computed under remarkably weak non-degeneracy conditions.

New Bounds for Hypercube Slicing Numbers - Ziegler, Martin; Emamy-Khansari, M. Reza (Proceedings of the First International Conference on Discrete Models - Combinatorics, Computation and Geometry (DM-CCG'2001))
What is the maximum number of edges of the d-dimensional hypercube, denoted by S(d,k), that can be sliced by k many hyperplanes? This question on combinatorial properties of Euclidean geometry arising from linear separability considerations in the theory of Perceptrons has become an issue on its own. We use computational and combinatorial methods to obtain new bounds on S(d,k), s<=8. These strengthen earlier results on hypercube cut numbers.

Turing Computability of (Non-)Linear Optimization - Brattka, Vasco; Ziegler, Martin (Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG'01))
We consider the classical LINEAR OPTIMIZATION Problem, but in the Turing rather than the RealRAM model. Asking for mere computability of a function's maximum over some closed domain, we show that the common presumptions 'full-dimensional' and `bounded' in fact cannot be omitted: The sound framework of Recursive Analysis enables us to rigorously prove this folkloristic observation! On the other hand, convexity of this domain may be weakened to connectedness, and even NON-linear functions turn out to be effectively optimizable.

Occlusion Culling for Virtual Environments based on the 3D-Sectorgraph - Klein, Jan; Fischer, Matthias (Proc. of 3. GI-Informatiktage 2001)
We present a new approximate occlusion-culling algorithm that in contrast to other algorithms, manages the objects of the scene in a 3D-sectorgraph. For generating a frame, as far as possible only the visible objects are rendered that can be found quickly by an edge of the graph. The algorithm allows a real-time navigation with over 20 frames per second in complex scenes consisting of over 10 millions of polygons. Moreover, approximation errors are very low.

The randomized z-buffer algorithm - Wand, Michael; Fischer, Matthias; Peter, Ingmar; Meyer auf der Heide, Friedhelm; Straßer, Wolfgang (Proceedings of the 28th annual conference on Computer graphics and interactive techniques - SIGGRAPH '01)
We present a new output-sensitive rendering algorithm, the randomized z-buffer algorithm. It renders an image of an arbitrary three-dimensional scene consisting of triangular primitives by reconstruction from a dynamically chosen set of random surface sample points. This approach is independent of mesh connectivity and topology. The resulting rendering time grows only logarithmically with the numbers of triangles in the scene. We were able to render walkthroughs of scenes of up to 10^14 triangles at interactive frame rates. Automatic identification of low detail scene components ensures that the rendering speed of the randomized z-buffer cannot drop below that of conventional z-buffer rendering. Experimental and analytical evidence is given that the image quality is comparable to that of common approaches like z-buffer rendering. The precomputed data structures employed by the randomized z-buffer allow for interactive dynamic updates of the scene. Their memory requirements grow only linearly with the number of triangles and allow for a scene graph based instantiation scheme to further reduce memory consumption.

Data Management in Networks - Meyer auf der Heide, Friedhelm (Graph-Theoretic Concepts in Computer Science)

Parallel Bridging Models and Their Impact on Algorithm Design - Meyer auf der Heide, Friedhelm; Wanka, Rolf (Computational Science - ICCS 2001)

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

Communication in Parallel Systems-Models, Algorithms and Implementations - Rieping, Ingo

Caching in Networks: Non-Uniform Algorithms and Memory Capacity Constraints - Westermann, Matthias

PUB-Library, Release 7.0, User Guide and Function Reference - Bonorden, Olaf; Rieping, Ingo; von Otte, Ingo; Juurlink, Bernhardus

Probabilistic Methods for Coordination Problems - Scheideler, Christian

Tradeoff analysis and architecture design of a hybrid hardware/software sorter - Bednara, M.; Beyer, O.; Teich, J.; Wanka, Rolf (Proc. Int. Conf. on Application Specific Systems, Architectures, and Processors (ASAP))

Efficient Communication Strategies for Ad Hoc Wireless Networks - Adler, Micah; Scheideler, Christian (Theory Comput. Syst.)

From Static to Dynamic Routing: Efficient Transformations of Store-and-Forward Protocols - Scheideler, Christian; Vöcking, Berthold (SIAM J. Comput.)

Distributed Path Selection for Storage Networks - Berenbrink, Petra; Brinkmann, André; Scheideler, Christian (PDPTA)

Coloring non-uniform hypergraphs: a new algorithmic approach to the general Lovász local lemma - Czumaj, Artur; Scheideler, Christian (SODA)

Coloring nonuniform hypergraphs: A new algorithmic approach to the general Lovász local lemma - Czumaj, Artur; Scheideler, Christian (Random Struct. Algorithms)

Efficient, distributed data placement strategies for storage area networks (extended abstract) - Brinkmann, André; Salzwedel, Kay; Scheideler, Christian (SPAA)

A new algorithm approach to the general Lovász local lemma with applications to scheduling and satisfiability problems (extended abstract) - Czumaj, Artur; Scheideler, Christian (STOC)

Randomized Point Sampling for Output-Sensitive Rendering of Complex Dynamic Scenes - Wand, Michael; Fischer, Matthias; Meyer auf der Heide, Friedhelm
We present a new output-sensitive rendering algorithm, the randomized z-buffer algorithm. It renders an image of a three dimensional scene of triangular primitives by reconstruction from a random sample of surface points which are chosen with a probability proportional to the projected area of the objects. The approach is independent of mesh connectivity and topology. It leads to a rendering time that grows only logarithmically with the numbers of triangles in the scene and to linear memory consumption, thus allowing walkthroughs of scenes of extreme complexity. We consider different methods for image reconstruction which aim at correctness, rendering speed and image quality and we develop an efficient data structure for sample extraction in output-sensitive time which allows for efficient dynamic updates of the scene. Experiments confirm that scenes consisting of some hundred billion triangles can be rendered within seconds with an image quality comparable to a conventional z-buffer rendering; in special cases, realtime performance can be achieved.

I/O-Efficient Well-Separated Pair Decomposition and Applications - Govindarajan, Sathish; Lukovszki, Tamas; Maheshwari, Anil; Zeh, Norbert (Proceedings of the 8th Annual European Symposium on Algorithms (ESA 2000), LNCS)

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.

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.

Computing Cut Numbers - Ziegler, Martin; Sohler, Christian (Proceedings of the 12th Canadian Conference on Computational Geometry (CCCG'00))
What is the minimum number of hyperplanes that slice all edges of the d-dimensional hypercube? The answers have been known for d<=4. This work settles the problem for d=5 and d=6. More precisely, a computer search implies that 4 hyperplanes do not suffice for this purpose (but 5 do). We also develop computational approaches for attacking this extremal problem from combinatorial geometry in higher dimensions. They allow us to determine for example all maximal sliceable subsets of hypercube edges up to dimension 7.

Periodification Scheme: Constructing Sorting Networks with Constant Period - Lorys, Krzysztof; Wanka, Rolf; Oesterdiekhoff, Brigitte; Kutylowski, Miroslaw (Journal of the ACM)
We consider comparator networks M that are used repeatedly: while the output produced by M is not sorted, it is fed again into M. Sorting algorithms working in this way are called periodic. The number of parallel steps performed during a single run of M is called its period, the sorting time of M is the total number of parallel steps that are necessary to sort in the worst case. Periodic sorting networks have the advantage that they need little hardware (control logic, wiring, area) and that they are adaptive. We are interested in comparator networks of a constant period, due to their potential applications in hardware design. Previously, very little was known on such networks. The fastest solutions required time O(nε) where the depth was roughly 1/ε. We introduce a general method called periodification scheme that converts automatically an arbitrary sorting network that sorts n items in time T(n) and that has layout area A(n) into a sorting network that has period 5, sorts ***(n • T(n) items in time O(T(<n)• log n), and has layout area O(A(n)) • T(n)). In particular, applying this scheme to Batcher's algorithms, we get practical period 5 comparator networks that sort in time O(log3n). For theoretical interest, one may use the AKS netork resulting in a period 5 comparator network with runtime O(log2n).

A New Algorithmic Approach to the General Lovász Local Lemma with Applications to Scheduling and Satisfiability Problems - Czumaj, Artur; Scheideler, Christian (32nd ACM Symposium on Theory of Computing)

Data management in hierarchical bus networks - Meyer auf der Heide, Friedhelm; Räcke, Harald; Westermann, Matthias (Proceedings of the twelfth annual ACM symposium on Parallel algorithms and architectures - SPAA '00)

Caching in networks - Meyer auf der Heide, Friedhelm; Vöcking, Berthold; Westermann, Matthias (SODA '00: Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms)
We present a general framework for the development of on-line algorithms for data management in networks with limited memory capacities. These algorithms dynamically create and delete copies of shared data objects that can be read and written by the nodes in the network. Our algorithms aim to minimize the congestion, i.e., the maximum communication load over all network resources, so that that none of these resources become a communication bottleneck. We give several examples of networks for which our framework yields efficient algorithms, including meshes, fat-trees, hypercubic networks, and complete networks. For example, our framework yields an $O(d cdot log n)$-competitive caching algorithm for $d$-dimensional meshes of size $n$ with respect to the congestion on the communication links, and an $O(1)$-competitive algorithms for complete networks with respect to the congestion at the memory modules due to remote accesses. Previous work on data management in networks either neglects memory capacity constraints or minimizes only the total communication load, i.e., the sum of the communication load over all resources, which may produce congestion as some of the links become bottlenecks.

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

Contention Resolution in Hashing Based Shared Memory Simulations - Czumaj, Artur; Meyer auf der Heide, Friedhelm; Stemann, Volker (SIAM Journal on Computing)

Von der Hollerith-Maschine zum Parallelrechner - Die alltägliche Aufgabe des Sortierens als Fortschrittsmotor für die Informatik - Meyer auf der Heide, Friedhelm; Wanka, Rolf (ForschungsForum Paderborn)

The Paderborn university BSP (PUB) library-design, implementation and performance - Bonorden, Olaf; Juurlink, Bernhardus; Von Otte, I.; Rieping, Ingo (Proceedings 13th International Parallel Processing Symposium and 10th Symposium on Parallel and Distributed Processing)
The Paderborn University BSP (PUB) library is a parallel C library based on the BSP model. The basic library supports buffered and unbuffered asynchronous communication between any pair of processors, and a mechanism for synchronizing the processors in a barrier style. In ad-dition, it provides routines for collective communication on arbitrary subsets of processors, partition operations, and a zero-cost synchronization mechanism. Furthermore, some techniques used in its implementation deviate significantly from the techniques used in other BSP libraries.

Simple, Efficient Routing Schemes for All-Optical Networks - Flammini, Michele; Scheideler, Christian (Theory Comput. Syst.)

Locally Efficient On-Line Strategies for Routing Packets Along Fixed Paths - Berenbrink, Petra; Scheideler, Christian (SODA)

Simple Competitive Request Scheduling Strategies - Berenbrink, Petra; Riedel, Marco; Scheideler, Christian (SPAA)

Partitioned neighborhood spanners of minimal outdegree - Fischer, Matthias; Lukovszki, Tamas; Ziegler, Martin (Proceedings of the 11th Canadian Conference on Computational Geometry)
A geometric spanner with vertex set P in Rd is a sparse approximation of the complete Euclidean graph determined by P. We introduce the notion of partitioned neighborhood graphs (PNGs), unifying and generalizing most constructions of spanners treated in literature. Two important parameters characterizing their properties are the outdegree k in N and the stretch factor f>1 describing the quality of approximation. PNGs have been throughly investigated with respect to small values of f. We present in this work results about small values of k. The aim of minimizing k rather than f arises from two observations: * k determines the amount of space required for storing PNGs. * Many algorithms employing a (previously constructed) spanner have running times depending on its outdegree. Our results include, for fixed dimensions d as well as asymptotically, upper and lower bounds on this optimal value of k. The upper bounds are shown constructively and yield efficient algorithms for actually computing the corresponding PNGs even in degenerate cases.

Fast Reconstruction of Delaunay Triangulations - Sohler, Christian (Proceedings of the 11th Canadian Conference on Computational Geometry ( CCCG'99))
We present a new ( O(n) ) algorithm to compute good orders for the point set of a Delaunay triangulation of ( n ) points in the plane. Such a good order makes reconstruction in ( O(n) ) time with a simple algorithm possible. In contrast to the algorithm of Snoeyink and van Kreveld cite1, which is based on independent sets, our algorithm uses a breadth first search (BFS) to obtain these orders. Both approaches construct such orders by repeatedly removing a constant fraction of vertices from the current triangulation. The advantage of the BFS approach is that we can give significantly better bounds on the fraction of removed points in a phase of the algorithm. We can prove that a single phase of our algorithm removes at least ( frac13 ) of the points, even if we restrict the degree of the points (at the time they are removed) to 6. We implemented and compared both algorithms. Our algorithms is slightly faster and achieves about 15% better vertex data compression when using a simple variable length code to encode the differences between two consecutive vertices of the given order.

New Results on Geometric Spanners and Their Applications - Lukovszki, Tamás

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.

Data management in networks: experimental evaluation of a provably good strategy - Krick, Christof; Meyer auf der Heide, Friedhelm; Räcke, Harald; Vöcking, Berthold; Westermann, Matthias (Proceedings of the eleventh annual ACM symposium on Parallel algorithms and architectures - SPAA '99)

Generating Random Star-Shaped Polygons - Sohler, Christian (Proceedings of the 11th Canadian Conference on Computational Geometry ('CCCG'99))
In this paper we deal with two problems on star-shaped polygons. First, we present a Las-Vegas algorithm that uniformly at random creates a star-shaped polygon whose vertices are given by a point set ( S ) of ( n ) points in the plane that does not admit degenerate star-shaped polygons. The expected running time of the algorithm is ( O(n^2log n) ) and it uses ( O(n) ) memory. We call a star-shaped polygon degenerate if its kernel has 0 area. Secondly, we show how to count all star-shaped polygons whose vertices are a subset of ( S ) in ( O(n^5log n) ) time and ( O(n) ) space. The algorithm can also be used for random uniform generation. We also present lower and upper bounds on the number of star-shaped polygons.

Design of the PRESTO Multimedia Storage Network (Extended Abstract) - Berenbrink, Petra; Riedel, Marco; Scheideler, Christian (International Workshop on Communication and Data Management in Large Networks (CDMLarge))

From Static to Dynamic Routing: Efficient Transformations of Store-and-Forward Protocols - Scheideler, Christian; Vöcking, Berthold (STOC)

Shortest-Path Routing in Arbitrary Networks - Meyer auf der Heide, Friedhelm; Vöcking, Berthold (Journal of Algorithms)

Allocating Weighted Jobs in Parallel - Berenbrink, P.; Meyer auf der Heide, Friedhelm; Schröder, K. (Theory of Computing Systems)

International Workshop on Communication and Data Management in Large Networks - Mayr, E. W.; Meyer auf der Heide, Friedhelm; Wanka, Rolf (Informatik aktuell)

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

Static and Dynamic Data Management in Networks - Vöcking, Berthold

The Paderborn University BSP (PUB) Library - Design, Implementation and Performance - Bonorden, Olaf; Rieping, Ingo; von Otte, Ingo; Juurlink, Bernhardus
The Paderborn University BSP (PUB) library is a parallel C library based on the BSP model. The basic library supports buffered and unbuffered asynchronous communication between any pair of processors, and a mechanism for synchronizing the processors in a barrier style. In addition, it provides routines for collective communication on arbitrary subsets of processors, partition operations, and a zero-cost synchronization mechanism. Furthermore, some techniques used in the implementation of the PUB library deviate significantly from the techniques used in other BSP libraries.

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.

A Network Based Approach for Realtime Walkthrough of Massive Models - Fischer, Matthias; Lukovszki, Tamas; Ziegler, Martin (Algorithm Engineering, 2nd International Workshop, WAE '98)
New dynamic search data structures developed recently guarantee constant execution time per search and update, i.e., they fulfil the real-time requirements necessary for interactive walkthrough in large geometric scenes. Yet, superiority or even applicability of these new methods in practice was still an open question. Their prototypical implementation presented in this work uses common libraries on standard stations and thus represents a first strut to bridge this gap. Indeed our experimental results give an indication on the actual performance of these theoretical ideas on real machines and possible bottlenecks in future developments. By special algorithmic enhancements, we can even avoid the otherwise essential preprocessing step.

Multimediale Entdeckungsreisen unserer Welt mit dem Internet - Ziegler, Martin; Fischer, Matthias; Lukovszki, Tamás
Preis für den Beitrag "Multimediale Entdeckungsreisen unserer Welt mit dem Internet"

On Periodic Comparator Networks - Oesterdiekhoff, Brigitte

Universal Continuous Routing Strategies - Scheideler, Christian; Vöcking, Berthold (Theory Comput. Syst.)

Efficient Communication Strategies for Ad-Hoc Wireless Networks (Extended Abstract) - Adler, Micah; Scheideler, Christian (SPAA)

Improved Bounds for Acyclic Job Shop Scheduling (Extended Abstract) - Feige, Uriel; Scheideler, Christian (STOC)

Universal Routing Strategies for Interconnection Networks - Scheideler, Christian

Routing on networks of optical crossbars - Meyer auf der Heide, Friedhelm; Schröder, Klaus; Schwarze, Frank (Theoretical Computer Science)

Truly efficient parallel algorithms: 1-optimal multisearch for an extension of the BSP model - Bäumker, Armin; Dittrich, Wolfgang; Meyer auf der Heide, Friedhelm (Theoretical Computer Science)

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

Randomized protocols for low-congestion circuit routing in multistage interconnection networks - Cole, Richard; Maggs, Bruce M.; Meyer auf der Heide, Friedhelm; Mitzenmacher, Michael; Richa, Andréa W.; Schröder, Klaus; Sitaraman, Ramesh K.; Vöcking, Berthold (Proceedings of the thirtieth annual ACM symposium on Theory of computing - STOC '98)

Communication Efficient Parallel Searching - Bäumker, Armin

Communication and I/O Efficient Parallel Data Structures - Dittrich, Wolfgang

Bounded Degree Spanning Trees - Strothmann, Willy-Bernhard

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 $dT$.

Decremental Biconnectivity on Planar Graphs - Strothmann, Willy-Bernhard; Lukovszki, Tamás
In this paper we present a (randomized) algorithm for maintaining the biconnected components of a dynamic planar graph of $n$ vertices under deletions of edges. The biconnected components can be maintained under any sequence of edge deletions in a total of $O(n log n)$ time, with high probability. This gives $O(log n)$ amortized time per edge deletion, which improves previous (deterministic) results due to Giammarresi and Italiano, where $O(n log^2 n)$ amortized time is needed. Our work describes a simplification of the data structures from [GiIt96] and uses dynamic perfect hashing to reduce the running time. As in the paper by Giammarresi and Italiano, we only need $O(n)$ space. Finally we describe some simply additional operations on the decremental data structure. By aid of them this the data structure is applicable for finding efficiently a $Delta$-spanning tree in a biconnected planar graph with a maximum degree $2Delta-2$ do to Czumaj and Strothmann.

Encoding a Triangulation as a Permutation of its Point Set - Sohler, Christian; Denny, Markus (Proceedings of the 9th Canadian Conference on Computational Geometry)

Optimal Wormhole Routing in the (n, d)-Torus - Bock, Stefan; Meyer auf der Heide, Friedhelm; Scheideler, Christian (IPPS)