@MISC{Csail_probabilisticembeddings, author = {Piotr Indykmit Csail}, title = {Probabilistic Embeddings of Bounded Genus Graphs IntoPlanar Graphs}, year = {} }

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Abstract

ABSTRACT A probabilistic C-embedding of a (guest) metric M into a collection of (host) metrics M01,..., M0k is a randomized mapping F of M into one of the M01,..., M0k such that, for any two points p, q in the guest metric: 1. The distance between F (p) and F (q) in any M 0i is not smaller than the original distance between p and q. 2. The expected distance between F (p) and F (q) in (random) M0i is not greater than some constant C times the original distance, for C> = 1. The constant C is called the distortion of the embedding. Low-distortion probabilistic embeddings enable reducing algorithmic problems over "hard " guest metrics into "easy " host metrics.