New Upper Bounds on Continuous Tree Edge-Partition Problem
We consider continuous tree edge-partition problem on a edge-weighted tree network. A continuous p-edge-partition of a tree is to divide it into p subtrees by selecting p − 1 cut points along the edges of the underlying tree. The objective is to maximize (minimize) the minimum (maximum) length of the subtrees. We present an O(nlog2 n)-time algorithm for the max-min problem which is based on parametric search technique  and an efficient solution to the ratio search problem. Similar algorithmic technique, when applied to the min-max problem, results in an O(nh T logn)-time algorithm where h T is the height of the underlying tree network. The previous results for both max-min and min-max problems are O(n 2) .
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