### 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 language | English (US) |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 70-81 |

Number of pages | 12 |

Volume | 4110 LNCS |

State | Published - 2006 |

Event | 9th 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 2006 → Aug 30 2006 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 4110 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2006 and 10th International Workshop on Randomization and Computation, RANDOM 2006 |
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Country | Spain |

City | Barcelona |

Period | 8/28/06 → 8/30/06 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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.

}

TY - GEN

T1 - A tight lower bound for the steiner point removal problem on trees

AU - Chan, T. H Hubert

AU - Xia, Donglin

AU - Konjevod, Goran

AU - Richa, Andrea

PY - 2006

Y1 - 2006

N2 - 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)).

AB - 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)).

UR - http://www.scopus.com/inward/record.url?scp=33750036089&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33750036089&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33750036089

SN - 3540380442

SN - 9783540380443

VL - 4110 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 70

EP - 81

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -