On Approximating Real-World Halting Problems - Köhler, Sven; Schindelhauer, Christian; Ziegler, Martin (Fundamentals of Computation Theory)

An Explicit Solution to Post’s Problem over the Reals - Meer, Klaus; Ziegler, Martin (Fundamentals of Computation Theory)

Computability and Continuity on the Real Arithmetic Hierarchy and the Power of Type-2 Nondeterminism - Ziegler, Martin (Proc. CiE 2005: New Computational Paradigms)
The sometimes so-called Main Theorem of Recursive Analysis implies that any computable real function is necessarily continuous. We consider three relaxations of this common notion of real computability for the purpose of treating also discontinuous functions f:R->R: *) non-deterministic computation; *) relativized computation, specifically given access to oracles like 0' or 0''; *) encoding input x and/or output y=f(x) in weaker ways according to the Real Arithmetic Hierarchy. It turns out that, among these approaches, only the first one provides the required power.

Dynamic Load Balancing in Distributed Hash Tables - Bienkowski, Marcin; Korzeniowski, Miroslaw; Meyer auf der Heide, Friedhelm (Peer-to-Peer Systems IV)

Page Migration in Dynamic Networks - Bienkowski, Marcin; Meyer auf der Heide, Friedhelm (Mathematical Foundations of Computer Science 2005)

A Web Computing Environment for Parallel Algorithms in Java - Bonorden, Olaf; Gehweiler, Joachim; Meyer auf der Heide, Friedhelm (Proceeedings of 6th International Conference on Parallel Processing and Applied Mathematics (PPAM))
We present a web computing library (PUBWCL) in Java that allows to execute strongly coupled, massively parallel algorithms in the bulk-synchronous (BSP) style on PCs distributed over the internet whose owners are willing to donate their unused computation power. PUBWCL is realized as a peer-to-peer system and features migration and restoration of BSP processes executed on it. The use of Java guarantees a high level of security and makes PUBWCL platform independent. In order to estimate the loss of efficiency inherent in such a Java-based system, we have compared it to our C-based PUB-Library.

Load Balancing Strategies in a Web Computing Environment - Bonorden, Olaf; Gehweiler, Joachim; Meyer auf der Heide, Friedhelm (Proceeedings of 6th International Conference on Parallel Processing and Applied Mathematics (PPAM))
We compare different load balancing strategies for Bulk-Synchronous Parallel (BSP) programs in a web computing environment. In order to handle the influence of the fluctuating available computation power, we classify the external work load. We evaluate the load balancing algorithms using our web computing library for BSP programs in Java (PUBWCL). Thereby we simulated the external work load in order to have repeatable testing conditions. With the best performing load balancing strategy we could save 39% of the execution time averaged and even up to 50% in particular cases.

Detecting Privacy Violations in Sensitive XML Databases - Böttcher, Stefan; Steinmetz, Rita (Secure Data Management, Second VLDB Workshop, SDM 2005)

The Ising Model: Simple Evolutionary Algorithms as Adaptation Schemes - Briest, Patrick; Brockhoff, Dimo; Degener, Bastian; Englert, Matthias; Gunia, Christian; Heering, Oliver; Jansen, Thomas; Leifhelm, Michael; Plociennik, Kai; Röglin, Heiko; Schweer, Andrea; Sudholt, Dirk; et al. (Parallel Problem Solving from Nature - PPSN VIII)

Provably Secure Masking of AES - Blömer, Johannes; Guajardo, Jorge; Krummel, Volker (Selected Areas in Cryptography)

A Generalized Wiener Attack on RSA - Blömer, Johannes; May, Alexander (Public Key Cryptography – PKC 2004)

Secret Exponent Attacks on RSA-type Schemes with Moduli N=p^{r}q - May, Alexander (Public Key Cryptography – PKC 2004)

Computing the RSA Secret Key Is Deterministic Polynomial Time Equivalent to Factoring - May, Alexander (Advances in Cryptology – CRYPTO 2004)

Extreme Points Under Random Noise - Damerow, Valentina; Sohler, Christian (Proceedings of the 12th European Symposium on Algorithms (ESA'04))
Given a point set P in the d-dimensional unit hypercube, we give upper bounds on the maximal expected number of extreme points when each point is perturbed by small random noise chosen independently for each point from the same noise distribution Δ. Our results are parametrized by the variance of the noise distribution. For large variance we essentially consider the average case for distribution Δ while for variance 0 we consider the worst case. Hence our results give upper bounds on the number of extreme points where our input distributions range from average case to worst case. Our main contribution is a rather general lemma that can be used to obtain upper bounds on the expected number of extreme points for a large class of noise distributions. We then apply this lemma to obtain explicit bounds for random noise coming from the Gaussian normal distribution of variance σ² and the uniform distribution in a hypercube of side length &epsilon. For these noise distributions we show upper bounds of O( (1/ σ )^d * log^3/2 * d - 1 n ) and O( ( (n log n) / ε )^d/(d+1) ), respectively. Besides its theoretical motivation our model is also motivated by the observation that in many applications of convex hull algorithms the input data is inherently noisy, e.g. when the data comes from physical measurement or imprecise arithmetic is used.

Fast Multipoint Evaluation of Bivariate Polynomials - Nüsken, Michael; Ziegler, Martin (Proc. 12th Annual Symposium on Algorithms (ESA'04))
We generalize univariate multipoint evaluation of polynomials of degree n at sublinear amortized cost per point. More precisely, it is shown how to evaluate a bivariate polynomial p of maximum degree less than n, specified by its n^2 coefficients, simultaneously at n^2 given points using a total of O(n^2.667) arithmetic operations. In terms of the input size N being quadratic in n, this amounts to an amortized cost of O(N^0.334) per point.

Spanners, Weak Spanners, and Power Spanners for Wireless Networks - Schindelhauer, Christian; Volbert, Klaus; Ziegler, Martin (Proc. of 15th Annual International Symposium on Algorithms and Computation (ISAAC'04))
For $c in REAL$, a $c$-spanner is a subgraph of a complete Euclidean graph satisfying that between any two vertices there exists a path of weighted length at most $c$ times their geometric distance. Based on this property to approximate a complete weighted graph, sparse spanners have found many applications, e.g., in FPTAS, geometric searching, and radio networks. For geometric searching, it turned out to suffice whether the radius rather than the length of some path between any two vertices is bounded relatively to their geometric distance; this is the defining property of weak spanners. Finally regarding radio network applications, a power spanner accounts for the total energy afforded for a wireless transmission with the requirement that the sum of the squares of the lengths of some path between any two planar vertices must be bounded relatively to the square of their geometric distance (or higher powers up to 6 or even 8). While it is known that any $c$-spanner is also both a weak $C_1$-spanner and a $C_2$-power spanner (for appropriate $C_1,C_2$ depending only on $c$ but not on the graph under consideration), we show that the converse fails: There exists a family of $c_1$-power spanners that are no weak $C$-spanners and also a family of weak $c_2$-spanners that are no $C$-spanners for any fixed $C$ (and thus no uniform spanners, either). However the deepest result of the present work reveals that, surprisingly, any weak spanner is also a uniform power spanner. We further generalize the latter notion by considering $(c,delta)$-power spanners where the sum of the $delta$-th powers of the lengths has to be bounded; so $(cdot,2)$-power spanners coincide with the usual power spanners and $(cdot,1)$-power spanners are classical spanners. Interestingly, these $(cdot,delta)$-power spanners form a strict hierarchy where the above results still hold for any $deltageq2$; some even hold for $delta>1$ while counterexamples reveal others to fail for $delta<2$. In fact we show that in general every self-similar curve of fractal dimension $d>delta$ is no $(C,delta)$-power spanner for any fixed $C$.

Labeling Smart Dust - Bansal, Vikas; Meyer auf der Heide, Friedhelm; Sohler, Christian (12th Annual European Symposium on Algorithms (ESA 2004))
Given n distinct points p1, p2, ... , pn in the plane, the map labeling problem with four squares is to place n axis-parallel equi-sized squares Q1, ... ,Qn of maximum possible size such that pi is a corner of Qi and no two squares overlap. This problem is NP-hard and no algorithm with approximation ratio better than 1/2 exists unless P = NP [10]. In this paper, we consider a scenario where we want to visualize the information gathered by smart dust, i.e. by a large set of simple devices, each consisting of a sensor and a sender that can gather sensor data and send it to a central station. Our task is to label (the positions of) these sensors in a way described by the labeling problem above. Since these devices are not positioned accurately (for example, they might be dropped from an airplane), this gives rise to consider the map labeling problem under the assumption, that the positions of the points are not fixed precisely, but perturbed by random noise. In other words, we consider the smoothed complexity of the map labeling problem. We present an algorithm that, under such an assumption and Gaussian random noise with sufficiently large variance, has linear smoothed complexity.

A Runtime Environment for Reconfigurable Hardware Operating Systems - Walder, Herbert; Platzner, Marco (Proceedings of the 14th International Conference on Field Programmable Logic and Applications (FPL))

Algorithmic Approaches for Storage Networks - Salzwedel, Kay A. (Algorithms for Memory Hierarchies)

New Partial Key Exposure Attacks on RSA - Blömer, Johannes; May, Alexander (Advances in Cryptology - CRYPTO 2003)

Fault Based Cryptanalysis of the Advanced Encryption Standard (AES) - Blömer, Johannes; Seifert, Jean-Pierre (Financial Cryptography)

Quasi-optimal Arithmetic for Quaternion Polynomials - Ziegler, Martin (Proc. 14th Annual International Symposium on Algorithms and Computation (ISAAC'03))
Fast algorithms for arithmetic on real or complex polynomials are well-known and have proven to be not only asymptotically efficient but also very practical. Based on FAST FOURIER TRANSFORM, they for instance multiply two polynomials of degree up to N or multi-evaluate one at N points simultaneously within quasi-linear time O(N polylog N). An extension to (and in fact the mere definition of) polynomials over fields R and C to the SKEW-field H of quaternions is promising but still missing. The present work proposes three approaches which in the commutative case coincide but for H turn out to differ, each one satisfying some desirable properties while lacking others. For each notion, we devise algorithms for according arithmetic; these are quasi-optimal in that their running times match lower complexity bounds up to polylogarithmic factors.

Fast Relative Approximation of Potential Fields - Ziegler, Martin (Lecture Notes in Computer Science)
Multi-evaluation of the Coulomb potential induced by N particles is a central part of N-body simulations. In 3D, known subquadratic time algorithms return approximations up to given ABSOLUTE precision. By combining data structures from Computational Geometry with fast polynomial arithmetic, the present work obtains approximations of prescribable RELATIVE error e>0 in time O(1/e*N*polylog N).

Congestion and Almost Invariant Sets in Dynamical Systems - Dellnitz, Michael; Preis, Robert (Lecture Notes in Computer Science)

A New Data Structure for the Nondominance Problem in Multi-objective Optimization - Schütze, Oliver (Lecture Notes in Computer Science)

Covering Pareto Sets by Multilevel Evolutionary Subdivision Techniques - Schütze, Oliver; Mostaghim, Sanaz; Dellnitz, Michael; Teich, Jürgen (Lecture Notes in Computer Science)

Testing Containment of XPath Expressions in Order to Reduce the Data Transfer to Mobile Clients - Böttcher, Stefan; Steinmetz, Rita (Advances in Databases and Information Systems, 7th East European Conference, ADBIS 2003)

A DTD Graph Based XPath Query Subsumption Test - Böttcher, Stefan; Steinmetz, Rita (Database and XML Technologies, First International XML Database Symposium, XSym 2003)

Heuristics for Online Scheduling Real-Time Tasks to Partially Reconfigurable Devices - Steiger, Christoph; Walder, Herbert; Platzner, Marco (Proceedings of the 13th International Conference on Field Programmable Logic and Applications (FPL))

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))

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

Lipirea în combinatie cu îmbinarile obtinute prin deformare - Hahn, O.; Koyro, M.; Meschut, Gerson (sudura)

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.

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

Hybridfügen – Grundlagen, Technologie, Anwendungen - Meschut, Gerson (DVM-Bericht 668)

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

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)

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.

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

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)