On the relation between the relative earth mover distance and the variation distance (an exposition)
نویسندگان
چکیده
In this note we present a proof that the variation distance up to relabeling is upperbounded by the “relative earth mover distance” (to be defined below). The relative earth mover distance was introduced by Valiant and Valiant [VV11], and was extensively used in their work. The foregoing claim was made in [VV11], but was not used there. The claim appears a special case of [VV15, Fact 1] (i.e., the case of τ = 0). The proof we present is merely an elaboration of (this special case of) the proof presented by Valiant and Valiant in [VV15, Apdx A].
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