Abstract
We present several approximation algorithms for the problem of embedding metric spaces into a line, and into the 2-dimensional plane. Among other results, we give an O(n)approximation algorithm for the problem of finding a line embedding of a metric induced by a given unweighted graph, that minimizes the (standard) multiplicative distortion. We give an improved Õ(n1/3) approximation for the case of metrics induced by unweighted trees.
Original language | English |
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Pages (from-to) | 454-473 |
Number of pages | 20 |
Journal | SIAM Journal on Discrete Mathematics |
Volume | 33 |
Issue number | 1 |
DOIs | |
State | Published - 2019 |
Bibliographical note
Publisher Copyright:© 2019 Society for Industrial and Applied Mathematics
Keywords
- Approximation algorithms
- Distortion
- Line
- Metric embeddings
- Sphere
ASJC Scopus subject areas
- General Mathematics