New Upper Bounds on Continuous Tree Edge-Partition Problem

Authors:
Robert Benkoczi;Binay Bhattacharya;Qiaosheng Shi
Affiliations:
Mathematics and Computer Science, University of Lethbridge, Lethbridge, Canada T1K 3M4;School of Computing Science, Simon Fraser University, Burnaby B.C., Canada V5A 1S6;School of Computing Science, Simon Fraser University, Burnaby B.C., Canada V5A 1S6
Venue:
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
Year:
2008

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Abstract

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 psubtrees by selecting p驴 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(nlog2n)-time algorithm for the max-min problem which is based on parametric search technique [7] and an efficient solution to the ratio search problem. Similar algorithmic technique, when applied to the min-max problem, results in an O(nhTlogn)-time algorithm where hTis the height of the underlying tree network. The previous results for both max-min and min-max problems are O(n2) [5].