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(nlogn+plog2nlog(n/p)) time. For all values of p, our algorithm
thus runs as fast as or faster than the most efficient O(nlog2n) time
algorithm obtained by applying Cole's speed-up technique [cole1987] to the
algorithm due to Megiddo and Tamir [megiddo1983], which has remained
unchallenged for nearly 30 years. Our other algorithm, which is more practical,
runs in O(nlogn+p2log2(n/p)) time, and when p=O(n) it is
faster than Megiddo and Tamir's O(nlog2nloglogn) time algorithm
[megiddo1983]