On notions of distortion and an almost minimum spanning tree with constant average distortion

Yair Bartal*, Arnold Filtser, Ofer Neiman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

This paper makes two main contributions: a construction of a near-minimum spanning tree with constant average distortion, and a general equivalence theorem relating two refined notions of distortion: scaling distortion and prioritized distortion. Scaling distortion provides improved distortion for 1−ϵ fractions of the pairs, for all ϵ simultaneously. A stronger version called coarse scaling distortion, has improved distortion guarantees for the furthest pairs. Prioritized distortion allows to prioritize the nodes whose associated distortions will be improved. We show that prioritized distortion is essentially equivalent to coarse scaling distortion via a general transformation. This equivalence is used to construct the near-minimum spanning tree with constant average distortion, and has many further implications to metric embeddings theory. Among other results, we obtain a strengthening of Bourgain's theorem on embedding arbitrary metrics into Euclidean space, possessing optimal prioritized distortion.

Original languageAmerican English
Pages (from-to)116-129
Number of pages14
JournalJournal of Computer and System Sciences
Volume105
DOIs
StatePublished - Nov 2019

Bibliographical note

Publisher Copyright:
© 2019 Elsevier Inc.

Keywords

  • Average distortion
  • Light spanner
  • Metric embedding
  • Prioritized distortion
  • Scaling distortion

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