TEL-AVIV UNIVERSITY RAYMOND AND BEVERLY SACKLER FACULTY OF EXACT SCIENCES BLAVATNIK SCHOOL OF COMPUTER SCIENCE The 2-Center Problem in Three Dimensions
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چکیده
Let P be a set of n points in three dimensions. The 2-center problem for P is to find two closed congruent balls with smallest radius which cover P . We present a randomized algorithm for solving the problem in O ( 1 (1−r∗/r0)3n 2 log n ) expected time, where r∗ is the common radius of the optimal solution balls and r0 is the radius of the smallest enclosing ball of P . This improves the naive solution, which takes O(n4) time, and (unless r∗ is very close to r0) also improves a simpler, nearly cubic algorithm, which we also present.
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