The euclidean bottleneck steiner path problem (original) (raw)

We consider a geometric optimization problem that arises in network design. Given a set P of n points in the plane, source and destination points s, t ∈ P , and an integer k > 0, one has to locate k Steiner points, such that the length of the longest edge of a bottleneck path between s and t is minimized. In this paper, we present an O(n log 2 n)-time algorithm that computes an optimal solution, for any constant k. This problem was previously studied by Hou et al. , who gave an O(n 2 log n)-time algorithm. We also study the dual version of the problem, where a value λ > 0 is given (instead of k), and the goal is to locate as few Steiner points as possible, so that the length of the longest edge of a bottleneck path between s and t is at most λ.