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 - THES AU - Lukovszki, Tamás ID - 18942 SN - 3-931466-62-0 TI - New Results on Geometric Spanners and Their Applications ER - TY - GEN AU - Eke, Norbert Otto ED - Max, Frank Rainer ED - Ruhrberg, Christine ID - 19461 T2 - Reclams Romanlexikon. Bd. 2: Von der Romantik bis zum Naturalismus TI - Nikolaus Lenau: Savonarola. Ein Gedicht; Die Albigenser. Freie Dichtungen ER - TY - JOUR AU - Steffen, Eckhard ID - 10189 JF - Graphs Comb. TI - Non-bicritical critical snarks VL - 15 ER - TY - JOUR AU - Hüllermeier, Eyke ID - 16199 IS - 5 JF - International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems TI - Numerical methods for fuzzy initial value problems VL - 7 ER - TY - CONF AB - We present an object-oriented approach based on the Unified Modeling Language (UML) for modeling structure and dynamic behavior of a multimedia information system. We extend the Model-View-Controller paradigm for interactive systems towards multimedia and show that aspects of the graphical user interface and time-dynamic behavior ought to be integral parts of a model. This is done in the intention of achieving a coherent model of a multimedia information system. As a result, we present OMMMA-L a UML-based language for the Object-Oriented Modeling of MultiMedia Applications. OMMMA-L deploys class and state diagrams of UML as well as an extended sequence diagram and a newly introduced presentation diagram to adequately specify the visual presentation within a multimedia information system. In addition to explaining the different diagram types, we also define pragmatic rules on how to deploy and combine the various diagrams. Additionally, we relate OMMMA-L to basic ideas of multimedia information systems. AU - Sauer, Stefan AU - Engels, Gregor ID - 8322 T2 - Proceedings of the workshop on Multimedia Information Systems (MIS 1999), Indian Wells, CA (USA) TI - OMMMA: An Object-Oriented Approach for Modeling Multimedia Information Systems ER - TY - GEN AU - Peckhaus, Volker ED - Cachro, Jacek ED - Kijania-Placek, Katarzyna ID - 17880 T2 - International Union of History and Philosophy of Science. 11th International Congress of Logic, Methodology and Philosophy of Science. Volume of Abstracts. August 20–26, 1999, Cracow, Poland TI - On Deepening Foundations: Hilbert’s Axiomatic Program Between Pragmatics and Naturalism [Abstract] ER - TY - JOUR AU - Dellnitz, Michael AU - Junge, Oliver ID - 16537 JF - SIAM Journal on Numerical Analysis SN - 0036-1429 TI - On the Approximation of Complicated Dynamical Behavior ER -