An Exact Algorithm for Minimum Distortion Embedding

  • Authors:

  • Fedor V. Fomin;Daniel Lokshtanov;Saket Saurabh

  • Affiliations:

  • Department of Informatics, University of Bergen, Bergen, Norway N-5020;Department of Informatics, University of Bergen, Bergen, Norway N-5020;Department of Informatics, University of Bergen, Bergen, Norway N-5020

  • Venue:
  • Graph-Theoretic Concepts in Computer Science
  • Year:
  • 2009

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Abstract

Let G be an unweighted graph on n vertices. We show that an embedding of the shortest path metric of G into the line with minimum distortion can be found in time 5 n + o(n). This is the first algorithm breaking the trivial n!-barrier.