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A Tight Lower Bound for the Steiner Point Removal Problem on Trees

  • T. -H. Hubert Chan
  • Donglin Xia
  • Goran Konjevod
  • Andrea Richa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4110)

Abstract

Gupta (SODA’01) considered the Steiner Point Removal (SPR) problem on trees. Given an edge-weighted tree T and a subset S of vertices called terminals in the tree, find an edge-weighted tree T S on the vertex set S such that the distortion of the distances between vertices in S is small. His algorithm guarantees that for any finite tree, the distortion incurred is at most 8. Moreover, a family of trees, where the leaves are the terminals, is presented such that the distortion incurred by any algorithm for SPR is at least 4(1 – o(1)). In this paper, we close the gap and show that the upper bound 8 is essentially tight. In particular, for complete binary trees in which all edges have unit weight, we show that the distortion incurred by any algorithm for the SPR problem must be at least 8 (1 – o(1)).

Keywords

Minor Mapping Outerplanar Graph Complete Binary Tree Minor Transformation Edge Contraction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • T. -H. Hubert Chan
    • 1
  • Donglin Xia
    • 2
  • Goran Konjevod
    • 2
  • Andrea Richa
    • 2
  1. 1.Computer Science DepartmentCarnegie Mellon University 
  2. 2.Department of Computer Science and EngineeringArizona State University 

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