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COMPGEOM

2010

ACM

2010

ACM

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...

Related Content

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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