Is there relations between earth mover's distance and vector norms?

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Say I have two vectors $a$ and $b$. Can I estimate $\mbox{EMD}(a,b)$ via some combination of things like $\|a-b\|_p$ and such?

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As far as I know, EMD is computed between to distribuions, not between vectors. By the way, here you have a LP formulation and more details

http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/RUBNER/emd.htm