TY - JOUR

T1 - A simple factor-2/3 approximation algorithm for two-circle point labeling

AU - Wolff, A.

AU - Thon, M.

AU - Xu, Y.F.

PY - 2002

Y1 - 2002

N2 - Given a set P of n points in the plane, the two-circle point-labeling problem consists of placing 2n uniform, non-intersecting, maximum-size open circles such that each point touches exactly two circles.
It is known that this problem is NP-hard to approximate. In this paper we give a simple algorithm that improves the best previously known approximation factor from to 2/3. The main steps of our algorithm are as follows. We first compute the Voronoi diagram, then label each point optimally within its cell, compute the smallest label diameter over all points and finally shrink all labels to this size. We keep the O(n log n) time and O(n) space bounds of the previously best algorithm.

AB - Given a set P of n points in the plane, the two-circle point-labeling problem consists of placing 2n uniform, non-intersecting, maximum-size open circles such that each point touches exactly two circles.
It is known that this problem is NP-hard to approximate. In this paper we give a simple algorithm that improves the best previously known approximation factor from to 2/3. The main steps of our algorithm are as follows. We first compute the Voronoi diagram, then label each point optimally within its cell, compute the smallest label diameter over all points and finally shrink all labels to this size. We keep the O(n log n) time and O(n) space bounds of the previously best algorithm.

U2 - 10.1142/S0218195902000888

DO - 10.1142/S0218195902000888

M3 - Article

VL - 12

SP - 269

EP - 282

JO - International Journal of Computational Geometry and Applications

JF - International Journal of Computational Geometry and Applications

SN - 0218-1959

IS - 4

ER -