The p-Center Problem in Tree Networks Revisited

We present two improved algorithms for weighted discrete p-center problem for tree networks with n vertices. One of our proposed algorithms runs in O(n logn + p log n log(n/p)) time. For all values of p, our algorithm thus runs as fast as or faster than the most efficient O(n log n) time algorithm obtained by applying Cole’s speed-up technique [10] to the algorithm due to Megiddo and Tamir [20], which has remained unchallenged for nearly 30 years. Our other algorithm, which is more practical, runs inO(n logn+p log(n/p)) time, and when p = O( √ n) it is faster than Megiddo and Tamir’s O(n log n log logn) time algorithm [20].