Dispersion in Unit Disks

We present two new approximation algorithms with (improved) constant ratios for selecting n points in n unit disks such that the minimum pairwise distance among the points is maximized. (I) A very simple O(n log n)-time algorithm with ratio 0.5110 for disjoint unit disks. In combination with an algorithm of Cabello [3], it yields a O(n2 )-time algorithm with ratio of 0.4487 for dispersion in n not necessarily disjoint unit disks. (II) A more sophisticated LP-based algorithm with ratio 0.6495 for disjoint unit disks that uses a linear number of variables and constraints, and runs in polynomial time. The algorithm introduces a novel technique which combines linear programming and projections for approximating distances. The previous best approximation ratio for disjoint unit disks was 1 2 . Our results give a partial answer to an open question raised by Cabello [3], who asked whether 1 2 could be improved.

• Type: Conference
• Year: 2010
• Where: STACS
• Authors: Adrian Dumitrescu, Minghui Jiang
• Keywords: Algorithm, Disjoint Unit Disks, Log N)-time Algorithm, STACS 2010, Theoretical Computer Science