New Upper Bounds on Continuous Tree Edge-Partition Problem

  • Robert Benkoczi
  • Binay Bhattacharya
  • Qiaosheng Shi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5034)

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 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(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 hT is the height of the underlying tree network. The previous results for both max-min and min-max problems are O(n2) [5].

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Robert Benkoczi
    • 1
  • Binay Bhattacharya
    • 2
  • Qiaosheng Shi
    • 2
  1. 1.Mathematics and Computer ScienceUniversity of LethbridgeLethbridgeCanada
  2. 2.School of Computing ScienceSimon Fraser UniversityBurnaby B.C.Canada

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