Regular ArticleThe 2-Center Problem with Obstacles☆
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Cited by (28)
Intersecting disks using two congruent disks
2023, Computational Geometry: Theory and ApplicationsCitation Excerpt :There are fair amounts of work on some variants of the 2-center problem, for example, on points and their centers lying outside input obstacles [16], on weighted points [12], on a convex polygon [25] in the plane, and on points in three dimensions [2].
Computing a geodesic two-center of points in a simple polygon
2019, Computational Geometry: Theory and ApplicationsCitation Excerpt :In this paper, we consider another variant of the k-center problem in which the set Q of m points are given in a simple n-gon P and the centers are constrained to lie in P. Here the boundary of the polygon P is assumed to act as an obstacle and the distance between any two points in P is thus measured by the length of the geodesic (shortest) path connecting them in P in contrast to [12]. We call this constrained version the geodesic k-center problem and its solution a geodesic k-center of Q with respect to P.
A simple linear algorithm for computing rectilinear 3-centers
2005, Computational Geometry: Theory and ApplicationsAn algorithmic framework for solving geometric covering problems - With applications
2014, International Journal of Foundations of Computer ScienceOn the Planar Two-Center Problem and Circular Hulls
2022, Discrete and Computational GeometryIntersecting Disks Using Two Congruent Disks
2021, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
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Work on this paper by Ken Goldberg and Dan Halperin has been supported by a grant from U.S.–Israeli Binational Science Foundation. Work by Dan Halperin and Micha Sharir has been supported by The Israel Science Foundation founded by the Israel Academy of Sciences and Humanities (Center for Geometric Computing and its Applications), by a Franco–Israeli research grant “factory of the future” (monitored by AFIRST/France and The Israeli Ministry of Science), and by the Hermann Minkowski–Minerva Center for Geometry at Tel Aviv University. A preliminay version of this paper appeared in Proceedings of the 16th ACM Symposium on Computational Geometry, Hong Kong, 2000, pp. 80–90.