@inproceedings{dfc3478159de46d28577697f248327fc,
title = "A tight lower bound for the steiner point removal problem on trees",
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 TS 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)).",
author = "Chan, {T. H Hubert} and Donglin Xia and Goran Konjevod and Andrea Richa",
year = "2006",
doi = "10.1007/11830924_9",
language = "English (US)",
isbn = "3540380442",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "70--81",
booktitle = "Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2006 a",
note = "9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2006 and 10th International Workshop on Randomization and Computation, RANDOM 2006 ; Conference date: 28-08-2006 Through 30-08-2006",
}