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The pp-Center Problem in Tree Networks Revisited

Abstract

We present two improved algorithms for weighted discrete pp-center problem for tree networks with nn vertices. One of our proposed algorithms runs in O(nlogn+plog2nlog(n/p))O(n \log n + p \log^2 n \log(n/p)) time. For all values of pp, our algorithm thus runs as fast as or faster than the most efficient O(nlog2n)O(n\log^2 n) 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))O(n \log n + p^2 \log^2(n/p)) time, and when p=O(n)p=O(\sqrt{n}) it is faster than Megiddo and Tamir's O(nlog2nloglogn)O(n \log^2n \log\log n) time algorithm [megiddo1983]

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