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

Oded Goldreich; Dana Ron

doi:10.1007/978-3-030-43662-9_9

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

Oded Goldreich^*, Dana Ron

^*Corresponding author for this work

School of Electrical Engineering

Weizmann Institute of Science

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-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 language	English
Title of host publication	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Publisher	Springer
Pages	141-151
Number of pages	11
DOIs	https://doi.org/10.1007/978-3-030-43662-9_9
State	Published - 2020

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12050 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

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10.1007/978-3-030-43662-9_9

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Goldreich, O., & Ron, D. (2020). On the relation between the relative earth mover distance and the variation distance (an exposition). In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 141-151). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12050 LNCS). Springer. https://doi.org/10.1007/978-3-030-43662-9_9

Goldreich, Oded ; Ron, Dana. / On the relation between the relative earth mover distance and the variation distance (an exposition). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer, 2020. pp. 141-151 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Goldreich, O & Ron, D 2020, On the relation between the relative earth mover distance and the variation distance (an exposition). in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12050 LNCS, Springer, pp. 141-151. https://doi.org/10.1007/978-3-030-43662-9_9

On the relation between the relative earth mover distance and the variation distance (an exposition). / Goldreich, Oded; Ron, Dana.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer, 2020. p. 141-151 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12050 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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Goldreich O, Ron D. On the relation between the relative earth mover distance and the variation distance (an exposition). In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer. 2020. p. 141-151. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-43662-9_9

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

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