A linear-time algorithm for radius-optimally augmenting paths in a metric space

Abstract

Let P be a path graph of n vertices embedded in a metric space. We consider the problem of adding a new edge to P to minimize the radius of the resulting graph. Previously, a similar problem for minimizing the diameter of the graph was solved in O(nlog n) time. To the best of our knowledge, the problem of minimizing the radius has not been studied before. In this paper, we present an O(n) time algorithm for the problem, which is optimal.