Massachusetts Institute of Technology Lecturer : Michel X . Goemans 18 . 409 : Topics in TCS : Embeddings of Finite Metric Spaces
نویسندگان
چکیده
Recall that a series-parallel graph consists of an edge, or of two series-parallel graphs connected in series or in parallel. A graph can be decomposed into series-parallel blocks if and only if it has treewidth 2. It is easy to see that these graphs cannot, in general, be embedded isometrically into `1: consider, for example, the n-cycle. In this lecture, we shall show two different constant-distortion embeddings of series-parallel graphs into `1, both due to [2].
منابع مشابه
Massachusetts Institute of Technology Michel X . Goemans 18 . 409 : Topics in TCS : Embeddings of Finite Metric Spaces
We will show how to obtain embeddings into `p with small dimension where all but an -fraction of the embedded distances have small distortion. This result has various applications in networking. The embedding is achieved by randomly choosing a small set of beacons, constructing a good embedding for these nodes (using, e.g., Borgain’s embedding), and then extending this embedding to the remainin...
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