TY - CHAP AU - Blömer, Johannes AU - Seifert, Jean-Pierre ID - 3018 SN - 0302-9743 T2 - Financial Cryptography TI - Fault Based Cryptanalysis of the Advanced Encryption Standard (AES) ER - TY - CONF AB - 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. AU - Ziegler, Martin ID - 18196 SN - 0302-9743 T2 - Proc. 14th Annual International Symposium on Algorithms and Computation (ISAAC'03) TI - Quasi-optimal Arithmetic for Quaternion Polynomials ER - TY - CHAP AB - 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). AU - Ziegler, Martin ED - Dehne, F. ED - Sack, JR. ED - Smid, M. ID - 18258 SN - 0302-9743 T2 - Lecture Notes in Computer Science TI - Fast Relative Approximation of Potential Fields VL - 2748 ER - TY - CHAP AU - Dellnitz, Michael AU - Preis, Robert ID - 16543 SN - 0302-9743 T2 - Lecture Notes in Computer Science TI - Congestion and Almost Invariant Sets in Dynamical Systems ER - TY - CHAP AU - Schütze, Oliver ID - 16664 SN - 0302-9743 T2 - Lecture Notes in Computer Science TI - A New Data Structure for the Nondominance Problem in Multi-objective Optimization ER - TY - CHAP AU - Schütze, Oliver AU - Mostaghim, Sanaz AU - Dellnitz, Michael AU - Teich, Jürgen ID - 16665 SN - 0302-9743 T2 - Lecture Notes in Computer Science TI - Covering Pareto Sets by Multilevel Evolutionary Subdivision Techniques ER - TY - CONF AU - Böttcher, Stefan AU - Steinmetz, Rita ID - 15077 SN - 0302-9743 T2 - Advances in Databases and Information Systems, 7th East European Conference, ADBIS 2003 TI - Testing Containment of XPath Expressions in Order to Reduce the Data Transfer to Mobile Clients ER - TY - CONF AU - Böttcher, Stefan AU - Steinmetz, Rita ID - 15078 SN - 0302-9743 T2 - Database and XML Technologies, First International XML Database Symposium, XSym 2003 TI - A DTD Graph Based XPath Query Subsumption Test ER - TY - CONF AU - Steiger, Christoph AU - Walder, Herbert AU - Platzner, Marco ID - 13615 SN - 0302-9743 T2 - Proceedings of the 13th International Conference on Field Programmable Logic and Applications (FPL) TI - Heuristics for Online Scheduling Real-Time Tasks to Partially Reconfigurable Devices ER - TY - CONF AU - Wanka, Rolf ID - 19850 SN - 0302-9743 T2 - Proc. Workshop on Graph-Theoretic Concepts in Computer Science (WG) TI - Any Load-Balancing Regimen for Evolving Tree Computations on Circulant Graphs Is Asymptotically Optimal ER - TY - CONF AU - Grünewald, Matthias AU - Lukovszki, Tamás AU - Schindelhauer, Christian AU - Volbert, Klaus ID - 24338 SN - 0302-9743 T2 - Proceedings of the 8th International Euro-Par Conference TI - Distributed Maintenance of Resource Efficient Wireless Network Topologies ER - TY - CONF AB - 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. AU - Adler, Micah AU - Räcke, Harald AU - Sivadasan, Naveen AU - Sohler, Christian AU - Vöcking, Berthold ID - 18566 SN - 0302-9743 T2 - Proceedings of the 29th International Colloquium on Automata, Languages and Programming TI - Randomized Pursuit-Evasion in Graphs ER - TY - CHAP AU - Meyer auf der Heide, Friedhelm AU - Kumar, Mohan AU - Nikoletseas, Sotiris AU - Spirakis, Paul ID - 16723 SN - 0302-9743 T2 - Euro-Par 2002 Parallel Processing TI - Mobile Computing, Mobile Networks ER - TY - JOUR AU - Czumaj, Artur AU - Sohler, Christian ID - 18749 JF - Proceedings of the 28th International Colloquium on Automata, Languages and Programming (ICALP) SN - 0302-9743 TI - Testing Hypergraph Coloring ER - TY - CONF AU - Lukovszki, Tamás AU - Maheshwari, Anil AU - Zeh, Norbert ID - 18964 SN - 0302-9743 T2 - Proceedings of the 21st Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2001), LNCS TI - I/O-Efficient Batched Range Counting and Its Applications to Proximity Problems ER - TY - CONF AB - 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. AU - Ziegler, Martin AU - Brattka, Vasco ID - 18152 SN - 0302-9743 T2 - Proceedings of the 4th Workshop on Computability and Complexity in Analysis (CCA'2000) TI - A Computable Spectral Theorem VL - 2064 ER - TY - CHAP AU - Meyer auf der Heide, Friedhelm ID - 16493 SN - 0302-9743 T2 - Graph-Theoretic Concepts in Computer Science TI - Data Management in Networks VL - 2204 ER - TY - CHAP AU - Meyer auf der Heide, Friedhelm AU - Wanka, Rolf ID - 16494 SN - 0302-9743 T2 - Computational Science - ICCS 2001 TI - Parallel Bridging Models and Their Impact on Algorithm Design ER - TY - BOOK ED - Meyer auf der Heide, Friedhelm ID - 16722 SN - 0302-9743 TI - Algorithms — ESA 2001, 9th Annual European Symposium Århus, Denmark ER - TY - CHAP AU - Blömer, Johannes ID - 3023 SN - 0302-9743 T2 - Automata, Languages and Programming TI - Closest Vectors, Successive Minima, and Dual HKZ-Bases of Lattices ER - TY - CONF AB - 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. AU - Czumaj, Artur AU - Sohler, Christian AU - Ziegler, Martin ID - 17990 SN - 0302-9743 T2 - Proceedings of the 8th Annual European Symposium on Algorithms (ESA'00) TI - Property Testing in Computational Geometry VL - 4698 ER - TY - CONF AB - 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. AU - Ziegler, Martin AU - Brattka, Vasco ID - 18146 SN - 0302-9743 T2 - SOFSEM 2000: Theory and Practice of Informatics TI - Computing the Dimension of Linear Subspaces VL - 1963 ER - TY - CHAP AU - Meyer auf der Heide, Friedhelm AU - Kutyłowski, Mirosław AU - Ragde, Prabhakar ID - 16497 SN - 0302-9743 T2 - Euro-Par 2000 Parallel Processing TI - Complexity Theory and Algorithms ER - TY - CHAP AU - Simon, Jens AU - Reinefeld, Alexander AU - Heinz, Oliver ED - Hellwagner, Hermann ED - Reinefeld, Alexander ID - 2435 SN - 0302-9743 T2 - SCI: Scalable Coherent Interface. Architecture and Software for High-Performance Compute Clusters TI - Large-Scale SCI Clusters in Practice: Architecture and Performance in SCI VL - 1734 ER - TY - CONF AB - 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. AU - Lukovszki, Tamás ID - 18959 SN - 0302-9743 T2 - Proceedings of the 6th Workshop on Algorithms an Data Structures (WADS'99), LNCS TI - New Results on Fault Tolerant Geometric Spanners ER - TY - CHAP AU - Meyer auf der Heide, Friedhelm AU - Vöcking, Berthold AU - Westermann, Matthias ID - 17053 SN - 0302-9743 T2 - Algorithms - ESA’ 99 TI - Provably Good and Practical Strategies for Non-uniform Data Management in Networks ER - TY - CONF AU - Eisenring, Michael AU - Platzner, Marco AU - Thiele, Lothar ID - 13608 SN - 0302-9743 T2 - Proceedings of the 9th International Workshop on Field Programmable Logic and Applications (FPL) TI - Communication Synthesis for Reconfigurable Embedded Systems VL - 1673 ER - TY - CHAP AB - 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. AU - Fischer, Matthias AU - Lukovszki, Tamás AU - Ziegler, Martin ID - 17412 SN - 0302-9743 T2 - Algorithms — ESA’ 98 TI - Geometric Searching in Walkthrough Animations with Weak Spanners in Real Time ER - TY - CHAP AU - Meyer auf der Heide, Friedhelm AU - Martinez, Gabriel Terán ID - 16562 SN - 0302-9743 T2 - LATIN'98: Theoretical Informatics TI - Communication-efficient parallel multiway and approximate minimum cut computation ER - TY - CONF AU - Platzner, Marco AU - De Micheli, Giovanni ID - 13606 SN - 0302-9743 T2 - Proceedings of the 8th International Workshop on Field Programmable Logic and Applications (FPL) TI - Acceleration of satisfiability algorithms by reconfigurable hardware ER - TY - CONF AB - 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 $dT$. AU - Czumaj, Artur AU - Strothmann, Willy-Bernhard ID - 19869 SN - 0302-9743 T2 - Proceedings of the Fifth Annual European Symposium on Algorithms (ESA'97) TI - Bounded degree spanning trees ER - TY - CHAP AU - Blömer, Johannes ID - 3029 SN - 0302-9743 T2 - Algorithms — ESA '97 TI - Denesting by bounded degree radicals ER - TY - CONF AB - 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. AU - Fischer, Matthias AU - Meyer auf der Heide, Friedhelm AU - Strothmann, Willy-Bernhard ID - 16568 SN - 0302-9743 T2 - 5th Annual European Symposium on Algorithms (ESA '97) TI - Dynamic data structures for realtime management of large geometric scenes VL - 1284 ER - TY - CHAP AU - Meyer auf der Heide, Friedhelm AU - Vöcking, Berthold ID - 16569 SN - 0302-9743 T2 - Euro-Par'97 Parallel Processing TI - Static and dynamic data management in networks ER - TY - CHAP AU - Bäumker, Armin AU - Meyer auf der Heide, Friedhelm ID - 16605 SN - 0302-9743 T2 - Solving Irregularly Structured Problems in Parallel TI - Communication efficient parallel searching ER - TY - CHAP AU - Karaivazoglou, Efstratios AU - Meyer auf der Heide, Friedhelm ID - 16687 SN - 0302-9743 T2 - Euro-Par'97 Parallel Processing TI - Routing on asyncronous processor networks ER - TY - CHAP AU - Kleine Büning, Hans AU - Lettmann, Theodor ID - 19816 SN - 0302-9743 T2 - Lecture Notes in Computer Science TI - Learning a representation for optimizable formulas ER - TY - CHAP AU - Bäumker, Armin AU - Dittrich, Wolfgang AU - Meyer auf der Heide, Friedhelm AU - Rieping, Ingo ID - 17564 SN - 0302-9743 T2 - Lecture Notes in Computer Science TI - Realistic parallel algorithms: Priority queue operations and selection for the BSP* Model ER - TY - BOOK ED - Meyer auf der Heide, Friedhelm ED - Monien, Burkhard ID - 16702 SN - 0302-9743 TI - Automata, Languages and Programming, 23rd International Colloquium, ICALP96 ER - TY - CHAP AU - Berenbrink, Petra AU - Meyer auf der Heide, Friedhelm AU - Stemann, Volker ID - 16703 SN - 0302-9743 T2 - STACS 96 TI - Fault-tolerant shared memory simulations ER - TY - CHAP AU - Meyer auf der Heide, Friedhelm AU - Vöcking, Berthold ID - 16704 SN - 0302-9743 T2 - STACS 95 TI - A packet routing protocol for arbitrary networks ER - TY - CHAP AU - Czumaj, Artur AU - Meyer auf der Heide, Friedhelm AU - Stemann, Volker ID - 16705 SN - 0302-9743 T2 - Lecture Notes in Computer Science TI - Shared memory simulations with triple-logarithmic delay ER - TY - CHAP AU - Meyer auf der Heide, Friedhelm AU - Westermann, Matthias ID - 16717 SN - 0302-9743 T2 - Graph-Theoretic Concepts in Computer Science TI - Hot-potato routing on multi-dimensional tori ER - TY - CHAP AU - Bäumker, Armin AU - Dittrich, Wolfgang AU - Meyer auf der Heide, Friedhelm ID - 16874 SN - 0302-9743 T2 - Lecture Notes in Computer Science TI - Truly efficient parallel algorithms: c-optimal multisearch for an extension of the BSP model ER - TY - BOOK ED - Meyer auf der Heide, Friedhelm ED - Monien, B. ED - Rosenberg, A. L. ID - 17477 SN - 0302-9743 TI - Parallel Architectures and Their Efficient Use ER - TY - CHAP AU - Meyer auf der Heide, Friedhelm AU - Oesterdiekhoff, Brigitte AU - Wanka, Rolf ID - 16730 SN - 0302-9743 T2 - Automata, Languages and Programming TI - Strongly adaptive token distribution ER - TY - CHAP AU - Lürwer-Brüggemeier, Katharina AU - Meyer auf der Heide, Friedhelm ID - 16732 SN - 0302-9743 T2 - Lecture Notes in Computer Science TI - Capabilities and complexity of computations with integer division ER - TY - CHAP AU - Alt, Helmut AU - Blömer, Johannes ID - 3046 SN - 0302-9743 T2 - Data structures and efficient algorithms TI - Resemblance and symmetries of geometric patterns ER - TY - CHAP AU - Dietzfelbinger, Martin AU - Meyer auf der Heide, Friedhelm ID - 16733 SN - 0302-9743 T2 - Data structures and efficient algorithms TI - High performance universal hashing, with applications to shared memory simulations ER - TY - CHAP AU - Meyer auf der Heide, Friedhelm ID - 16734 SN - 0302-9743 T2 - Lecture Notes in Computer Science TI - Hashing strategies for simulating shared memory on distributed memory machines ER - TY - CHAP AU - Meyer auf der Heide, Friedhelm AU - Pham, Hieu Thien ID - 16735 SN - 0302-9743 T2 - STACS 92 TI - On the performance of networks with multiple busses ER - TY - CHAP AU - Meyer auf der Heide, Friedhelm ID - 16789 SN - 0302-9743 T2 - STACS 89 TI - Computing minimum spanning forests on 1- and 2-dimensional processor arrays ER - TY - CHAP AU - Just, Bettina AU - Mathematik, Fb AU - Meyer auf der Heide, Friedhelm AU - Informatik, Fb AU - Wigderson, Avi ID - 16767 SN - 0302-9743 T2 - STACS 88 TI - On computations with integer division ER - TY - CHAP AU - Dietzfelbinger, M. AU - Mehlhorn, K. AU - Meyer auf der Heide, Friedhelm AU - Rohnert, H. ID - 16768 SN - 0302-9743 T2 - SWAT 88 TI - Upper and lower bounds for the dictionary problem ER - TY - CHAP AU - Büning, Hans Kleine AU - Lettmann, Theodor ED - Börger, Egon ID - 19821 SN - 0302-9743 T2 - Computation Theory and Logic TI - Representation independent query and update operations on propositional definite Horn formulas ER - TY - CHAP AU - Kleine Büning, H. AU - Lettmann, Theodor ID - 19819 SN - 0302-9743 T2 - 8th International Conference on Automated Deduction TI - Classes of first order formulas under various satisfiability definitions ER - TY - CHAP AU - Borodin, Allan AU - Fich, Faith E. AU - Meyer auf der Heide, Friedhelm AU - Upfal, Eli AU - Wigderson, Avi ID - 16774 SN - 0302-9743 T2 - Automata, Languages and Programming TI - A tradeoff between search and update time for the implicit dictionary problem ER - TY - CHAP AU - Meyer auf der Heide, Friedhelm ID - 16775 SN - 0302-9743 T2 - STACS 86 TI - Speeding up random access machines by few processors ER - TY - CHAP AU - Borodin, A. AU - Fich, F. AU - Meyer auf der Heide, Friedhelm AU - Upfal, E. AU - Wigderson, A. ID - 16776 SN - 0302-9743 T2 - STACS 86 TI - A time-space tradeoff for element distinctness ER - TY - CHAP AU - Meyer auf der Heide, Friedhelm ID - 16787 SN - 0302-9743 T2 - STACS 84 TI - Efficient simulations among several models of parallel computers (extended abstract) ER - TY - CHAP AU - Meyer auf der Heide, Friedhelm AU - Rollik, Anton ID - 16813 SN - 0302-9743 T2 - Fundamentals of Computation Theory TI - Random access machines and straight-line programs ER - TY - CHAP AU - Meyer auf der Heide, Friedhelm ID - 16814 SN - 0302-9743 T2 - Lecture Notes in Computer Science TI - Time-processor trade-offs for universal parallel computers ER -