On the Fermat-Weber center of a convex object Academic Article uri icon


  • We show that for any convex object Q in the plane, the average distance from the Fermat–Weber center of Q to the points in Q is at least , where is the diameter of Q, and that there exists a convex object P for which this distance is . We use this result to obtain a linear-time approximation scheme for finding an approximate Fermat–Weber center of a convex polygon Q.

publication date

  • November 1, 2005