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 $C$. AU - Schindelhauer, Christian AU - Volbert, Klaus AU - Ziegler, Martin ID - 18279 SN - 0302-9743 T2 - Proc. of 15th Annual International Symposium on Algorithms and Computation (ISAAC'04) TI - Spanners, Weak Spanners, and Power Spanners for Wireless Networks VL - 3341 ER - TY - JOUR AU - Tophinke, Doris ID - 18281 JF - Infodienst. Kulturpädagogische Nachrichten TI - Quatschwörterverse und Satzklötze. Sprachförderung im Kindergarten VL - 71 ER - TY - CONF AB - The visualisation of manufacturing-processes assists the user in understanding and analysis. Typically he can move free and unguided in a virtual environment which visualizes the entire process. Thus knowledge and conclusions are to some extend acquired on a random base. This article describes the development of a tool, which enables the user to interactively improve significant production processes in the simulation. He moves in a virtual 3D-environment (walkthrough system) and is able to acquire automatically calculated indications for significant processes. At the same time the simulation considers significant objects in a more detailed way. If the viewer is interested in a significant process, he is automatically guided to the relevant location where he can examine the critical situation by modification of the simulation model. AU - Mueck, Bengt AU - Dangelmaier, Wilhelm AU - Laroque, Christoph AU - Fischer, Matthias AU - Kortenjan, Michael ID - 18364 T2 - Simulation and Visualisation 2004 TI - Guidance of Users in Interactive 3D-Visualisations of Material Flow Simulations ER -