Coordinating the Motion of Several Discs

Cover Coordinating the Motion of Several Discs
Coordinating the Motion of Several Discs
Chee K Yap
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) Let fl be the complement of S and for simplicity, we assume SI is boimdcd (our results can be modified to hold even if fl is unbounded). Let B = (5i, . . . , B„) where fly is an (open) disc of radius r, . A placcmens p = (p^. . . . , p^) of B is a sequence of m points in Ci where /?/ specifies the center of fl;. B is assmned fized (with m = 2 or 3 in this paper) so that the input to the problera is a description of 5 and the initial and final placements of B. As in [IC], the boundary of 5 is ...decomposed into a collection of pairwise disjoint set of elements where an elsment is. Cither an open line segment (called a Svall') or a point ('comer'). The Input size h proportional to n, the number of comers in the boundary of 5. For any point x, let 5f(x) denote the set of points y occupied by 5/ when placed at x, ie. , the dii- tancc between y and x is

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