Title :
Planar Earthmover is not in L_1
Author :
Naor, Assaf ; Schechtman, Gideon
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 sube Ropf2 incurs distortion Omega(radic;(log n)). We also use Fourier analytic techniques to construct a simple L1 embedding of this space which has distortion O(log n)
Keywords :
Fourier analysis; computational complexity; computational geometry; probability; Fourier analytic technique; planar Earthmover; probability; transportation cost metric; Computer graphics; Computer science; Computer vision; Cost function; Distortion measurement; Extraterrestrial measurements; Labeling; Nearest neighbor searches; Probability distribution; Transportation;
Conference_Titel :
Foundations of Computer Science, 2006. FOCS '06. 47th Annual IEEE Symposium on
Conference_Location :
Berkeley, CA
Print_ISBN :
0-7695-2720-5
DOI :
10.1109/FOCS.2006.60
