Planar earthmover is not in L1

Assaf Naor, Gideon Schechtman

Research output: Contribution to journalArticle

Abstract

We show that any L1 embedding of the transportation cost (a.k.a. Earthmover) metric on probability measures supported on the grid {0,1,..., n}2 ⊆ ℝ2 incurs distortion Ω (√log n). We also use Fourier analytic techniques to construct a simple L1 embedding of this space which has distortion O(log n).

Original languageEnglish (US)
Pages (from-to)804-826
Number of pages23
JournalSIAM Journal on Computing
Volume37
Issue number3
DOIs
StatePublished - 2007

Fingerprint

Probability Measure
Grid
Metric
Costs

Keywords

  • Earthmover metric
  • Metric embeddings
  • Nearest neighbor search

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

Planar earthmover is not in L1 . / Naor, Assaf; Schechtman, Gideon.

In: SIAM Journal on Computing, Vol. 37, No. 3, 2007, p. 804-826.

Research output: Contribution to journalArticle

Naor, A & Schechtman, G 2007, 'Planar earthmover is not in L1 ', SIAM Journal on Computing, vol. 37, no. 3, pp. 804-826. https://doi.org/10.1137/05064206X
Naor, Assaf ; Schechtman, Gideon. / Planar earthmover is not in L1 . In: SIAM Journal on Computing. 2007 ; Vol. 37, No. 3. pp. 804-826.
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