### 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 | Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2006 a |

Publisher | Springer Verlag |

Pages | 70-81 |

Number of pages | 12 |

ISBN (Print) | 3540380442, 9783540380443 |

State | Published - Jan 1 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) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### 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 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2006 a*(pp. 70-81). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4110 LNCS). Springer Verlag.