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.
Bibliographical noteFunding 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.
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 (firstname.lastname@example.org). ‡Edgestream Partners L. P., Princeton, NJ 08540 (email@example.com). §Google Inc., Mountain View, CA 94043 (firstname.lastname@example.org). ¶Department of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213 (anupamg@ cs.cmu.edu). ‖MIT, Cambridge, MA 02139 (email@example.com). #Department of Computer Science, University of Haifa, Haifa, Israel (firstname.lastname@example.org). ††Technische Universität München, München, Germany (email@example.com). ‡‡CMU, Pittsburgh, PA 15213 (firstname.lastname@example.org).
© 2019 Society for Industrial and Applied Mathematics
- Approximation algorithms
- Metric embeddings
ASJC Scopus subject areas
- Mathematics (all)