A tight lower bound for the steiner point removal problem on trees

T. H Hubert Chan, Donglin Xia, Goran Konjevod, Andrea Richa

Research output: Chapter in Book/Report/Conference proceedingConference contribution

19 Citations (Scopus)

Abstract

Gupta (SODA'01) considered the Steiner Point Removal (SPR) problem on trees. Given an edge-weighted tree T and a subset 5 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)).

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages70-81
Number of pages12
Volume4110 LNCS
StatePublished - 2006
Event9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2006 and 10th International Workshop on Randomization and Computation, RANDOM 2006 - Barcelona, Spain
Duration: Aug 28 2006Aug 30 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4110 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2006 and 10th International Workshop on Randomization and Computation, RANDOM 2006
CountrySpain
CityBarcelona
Period8/28/068/30/06

Fingerprint

Steiner Point
Lower bound
Family Leave
Binary trees
Pedigree
Binary Tree
Leaves
Weights and Measures
Upper bound
Unit
Subset
Vertex of a graph

ASJC Scopus subject areas

  • Computer Science(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Theoretical Computer Science

Cite this

Chan, T. H. H., Xia, D., Konjevod, G., & Richa, A. (2006). A tight lower bound for the steiner point removal problem on trees. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4110 LNCS, pp. 70-81). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4110 LNCS).

A tight lower bound for the steiner point removal problem on trees. / Chan, T. H Hubert; Xia, Donglin; Konjevod, Goran; Richa, Andrea.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4110 LNCS 2006. p. 70-81 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4110 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Chan, THH, Xia, D, Konjevod, G & Richa, A 2006, A tight lower bound for the steiner point removal problem on trees. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 4110 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4110 LNCS, pp. 70-81, 9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2006 and 10th International Workshop on Randomization and Computation, RANDOM 2006, Barcelona, Spain, 8/28/06.
Chan THH, Xia D, Konjevod G, Richa A. A tight lower bound for the steiner point removal problem on trees. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4110 LNCS. 2006. p. 70-81. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Chan, T. H Hubert ; Xia, Donglin ; Konjevod, Goran ; Richa, Andrea. / A tight lower bound for the steiner point removal problem on trees. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4110 LNCS 2006. pp. 70-81 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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