We provide an approximation algorithm for selecting centers in a complete graph so as to minimize the maximum ratio of the distance between any two nodes via their respective centers to their true graph distance. Placing centers under such an objective function is important in designing efficient communication networks which rely on hubs for routing.

We give a direct combinatorial O(n³logn) algorithm for minimizing the number of late jobs on a single machine when jobs have release times and preemptions are allowed. Our algorithm improves the earlier O(n⁵) and O(n⁴) dynamic programming algorithms for this problem.