Two optimization problems for unit disks

Abstract

We present an implementation of a recent algorithm to compute shortest-path trees in unit disk graphs in O(n log n) worst-case time, where n is the number of disks.In the minimum-separation problem, we are given n unit disks and two points s and t, not contained in any of the disks, and we want to compute the minimum number of disks one needs to retain so that any curve connecting s to t intersects some of the retained disks. We present a new algorithm solving this problem in O(n 2 log 3 n) worst-case time and its implementation.