Topological stability of kinetic k-centers
نویسندگان
چکیده
We study the k -center problem in a kinetic setting: given set of continuously moving points P plane, determine (moving) disks that cover at every time step, such are as small possible any point time. Whereas optimal solution over may exhibit discontinuous changes, many practical applications require to be stable : must move smoothly Existing results on this with bounded speed, but model allows positive only for < 3 . Hence, limited and offer little theoretical insight. Instead, we topological stability -centers. Topological was recently introduced simply requires change continuously, do so arbitrarily fast. prove upper lower bounds ratio between radii an unstable topologically solution—the ratio—considering various metrics optimization criteria. For = 2 provide tight bounds, > can obtain nontrivial bounds. Finally, algorithm compute polynomial constant
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2021
ISSN: ['1879-2294', '0304-3975']
DOI: https://doi.org/10.1016/j.tcs.2021.03.026