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.}, author = {Lukovszki, Tamás}, booktitle = {Proceedings of the 6th Workshop on Algorithms an Data Structures (WADS'99), LNCS}, isbn = {9783540662792}, issn = {0302-9743}, pages = {193--204}, title = {{New Results on Fault Tolerant Geometric Spanners}}, doi = {10.1007/3-540-48447-7_20}, year = {1999}, } @phdthesis{18942, author = {Lukovszki, Tamás}, isbn = {3-931466-62-0 }, title = {{New Results on Geometric Spanners and Their Applications}}, year = {1999}, } @misc{19461, author = {Eke, Norbert Otto}, booktitle = {Reclams Romanlexikon. Bd. 2: Von der Romantik bis zum Naturalismus}, editor = {Max, Frank Rainer and Ruhrberg, Christine}, pages = {235--238}, publisher = {Reclam}, title = {{Nikolaus Lenau: Savonarola. Ein Gedicht; Die Albigenser. Freie Dichtungen}}, year = {1999}, } @article{10189, author = {Steffen, Eckhard}, journal = {Graphs Comb.}, pages = { 473--480}, title = {{Non-bicritical critical snarks}}, volume = {15}, year = {1999}, } @article{16199, author = {Hüllermeier, Eyke}, journal = {International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems}, number = {5}, pages = {439--461}, title = {{Numerical methods for fuzzy initial value problems}}, volume = {7}, year = {1999}, } @inproceedings{8322, abstract = {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.}, author = {Sauer, Stefan and Engels, Gregor}, booktitle = {Proceedings of the workshop on Multimedia Information Systems (MIS 1999), Indian Wells, CA (USA)}, pages = {64--71}, title = {{OMMMA: An Object-Oriented Approach for Modeling Multimedia Information Systems}}, year = {1999}, } @inproceedings{17880, author = {Peckhaus, Volker}, booktitle = {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}, editor = {Cachro, Jacek and Kijania-Placek, Katarzyna}, pages = {447}, publisher = {The Faculty of Philosophy, Jagiellonian University}, title = {{On Deepening Foundations: Hilbert’s Axiomatic Program Between Pragmatics and Naturalism [Abstract]}}, year = {1999}, } @article{16537, author = {Dellnitz, Michael and Junge, Oliver}, issn = {0036-1429}, journal = {SIAM Journal on Numerical Analysis}, pages = {491--515}, title = {{On the Approximation of Complicated Dynamical Behavior}}, doi = {10.1137/s0036142996313002}, year = {1999}, }