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949 results on '"Nakano, Shin-ichi"'

178. A freshwater radiation of diplonemids

Author

Mukherjee, Indranil, primary, Salcher, Michaela M., additional, Andrei, Adrian‐Ştefan, additional, Kavagutti, Vinicius Silva, additional, Shabarova, Tanja, additional, Grujčić, Vesna, additional, Haber, Markus, additional, Layoun, Paul, additional, Hodoki, Yoshikuni, additional, Nakano, Shin‐ichi, additional, Šimek, Karel, additional, and Ghai, Rohit, additional

Published
2020
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197. Topological Stability of Kinetic k-centers

Author

van der Hoog, Ivor, van Kreveld, Marc, Meulemans, Wouter, Verbeek, Kevin, Wulms, Jules, Nakano, Shin-ichi, Das, Gautam K., Mandal, Partha S., Mukhopadhyaya, Krishnendu, Sub Geometric Computing, Geometric Computing, Algorithms, Applied Geometric Algorithms, Algorithmic Spatial Data Analysis, EAISI Health, EAISI Foundational, and Algorithms, Geometry and Applications

Subjects
Computational Geometry (cs.CG), FOS: Computer and information sciences, General Computer Science, 0102 computer and information sciences, 02 engineering and technology, Topology, 01 natural sciences, Stability (probability), Upper and lower bounds, Theoretical Computer Science, Taverne, 0202 electrical engineering, electronic engineering, information engineering, Time-varying data, Facility location, Point (geometry), Time complexity, Mathematics, Plane (geometry), Stability analysis, Cover (topology), 010201 computation theory & mathematics, Bounded function, Computer Science - Computational Geometry, 020201 artificial intelligence & image processing, Mobile facility location, F.2.2, Constant (mathematics)
Abstract

We study the k-center problem in a kinetic setting: given a set of continuously moving points P in the plane, determine a set of k (moving) disks that cover P at every time step, such that the disks are as small as possible at any point in time. Whereas the optimal solution over time may exhibit discontinuous changes, many practical applications require the solution to be stable: the disks must move smoothly over time. Existing results on this problem require the disks to move with a bounded speed, but this model allows positive results only for k 3 . Hence, the results are limited and offer little theoretical insight. Instead, we study the topological stability of k-centers. Topological stability was recently introduced and simply requires the solution to change continuously, but may do so arbitrarily fast. We prove upper and lower bounds on the ratio between the radii of an optimal but unstable solution and the radii of a topologically stable solution—the topological stability ratio—considering various metrics and various optimization criteria. For k = 2 we provide tight bounds, and for small k > 2 we can obtain nontrivial lower and upper bounds. Finally, we provide an algorithm to compute the topological stability ratio in polynomial time for constant k.

Published
2019

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