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COMPGEOM
2010
ACM

The 2-center problem in three dimensions

13 years 8 months ago
The 2-center problem in three dimensions
Let P be a set of n points in R3 . The 2-center problem for P is to find two congruent balls of the minimum radius whose union covers P. We present two randomized algorithms for computing a 2-center of P. The first algorithm runs in O(n3 log8 n) expected time, and the second algorithm runs in O(n2 log8 n/(1−r∗ /r0)3 ) expected time, where r∗ is the radius of the 2-center of P and r0 is the radius of the smallest enclosing ball of P. The second algorithm is faster than the first one as long as r∗ is not very close to r0, which is equivalent to the condition of the centers of the two balls in the 2-center of P not being very close to each other. Categories and Subject Descriptors F.2.2 [Analysis of algorithms and problem complexity]: Nonnumerical algorithms and problems—Geometrical problems and computations; I.5.3 [Pattern recognition]: Clustering—algorithms General Terms Algorithms, Theory Keywords 2-center problem, facility location, geometric optimization, intersection...
Pankaj K. Agarwal, Rinat Ben Avraham, Micha Sharir
Added 10 Jul 2010
Updated 10 Jul 2010
Type Conference
Year 2010
Where COMPGEOM
Authors Pankaj K. Agarwal, Rinat Ben Avraham, Micha Sharir
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