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On the relation between the relative earth mover distance and the variation distance (an exposition)

Oded Goldreich, Dana Ron

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

The “relative earth mover distance” is a technical term introduced by Valiant and Valiant (43rd STOC, 2011), and extensively used in their work. They claimed that, for every two distributions, the relative earth mover distance upper-bounds the variation distance up to relabeling, but this claim was not used in their work. The claim appears as a special case of a result proved by Valiant and Valiant in a later work (48th STOC, 2016), but we found their proof too terse. The proof presented here is merely an elaboration of (this special case of) their proof.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsOded Goldreich
PublisherSpringer Verlag
Chapter9
Pages141-151
Number of pages11
DOIs
StatePublished - 4 Apr 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12050 LNCS

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science

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