CSE 599 I : Geometric embeddings ( Winter 2007 ) Instructor :
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چکیده
(a) Show that the 3-pointed star metric (S, d) does not embed isometrically (i.e. with distortion 1) into `2. The star metric has four points S = {c, v1, v2, v3} (a center and 3 leaves) with d(c, vi) = 1 for i = 1, 2, 3 and d(vi, vj) = 2 for i 6= j. (b) Show that (S, d) does embed isometrically into `1. (c) Let T = (V, E) be a graph-theoretic tree, and let dT be the (unweighted) shortest path metric on T . Show that (V, dT ) embeds isometrically into ` |E| 1 .
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تاریخ انتشار 2007