Approximation algorithms for low-distortion embeddings into low-dimensional spaces

Anastasios Sidiropoulos, Mihai Badoiu, Kedar Dhamdhere, Anupam Gupta, Piotr Indyk, Yuri Rabinovich, Harald Racke, And R. Ravi

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)454-473
Number of pages20
JournalSIAM Journal on Discrete Mathematics
Volume33
Issue number1
DOIs
StatePublished - 2019

Bibliographical note

Funding Information:
∗Received by the editors January 25, 2017; accepted for publication (in revised form) January 22, 2019; published electronically March 7, 2019. http://www.siam.org/journals/sidma/33-1/M111352.html Funding: The second, sixth, and seventh authors were supported by NSF ITR grants CCR-0085982 and CCR-0122581. The seventh author was also supported by NSF and NSF CCF 04-30751.

Funding Information:
The eighth author was supported by the Paris Kanellakis Fellowship Fund, the Alexandros S. Onassis Public Benefit Foundation, and by the National Science Foundation under grant CCF-1423230 and award CAREER-1453472. †Department of Computer Science, University of Illinois at Chicago, Chicago, IL 60607 (sidiropo@gmail.com). ‡Edgestream Partners L. P., Princeton, NJ 08540 (mihai@mit.edu). §Google Inc., Mountain View, CA 94043 (kedar@cs.cmu.edu). ¶Department of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213 (anupamg@ cs.cmu.edu). ‖MIT, Cambridge, MA 02139 (indyk@mit.edu). #Department of Computer Science, University of Haifa, Haifa, Israel (yuri@cslx.haifa.ac.il). ††Technische Universität München, München, Germany (harald.raecke@tum.de). ‡‡CMU, Pittsburgh, PA 15213 (ravi@andrew.cmu.edu).

Publisher Copyright:
© 2019 Society for Industrial and Applied Mathematics

Keywords

  • Approximation algorithms
  • Distortion
  • Line
  • Metric embeddings
  • Sphere

ASJC Scopus subject areas

  • Mathematics (all)

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