The geometry of graphs and some of its algorithmic applications
Linial, N.; London, E.; Rabinovich, Y.
Foundations of Computer Science, 1994 Proceedings., 35th Annual Symposium on
Volume , Issue , 20-22 Nov 1994 Page(s):577 - 591
Digital Object Identifier   10.1109/SFCS.1994.365733
Summary:We explore some implications of viewing graphs as geometric objects. This approach offers a new perspective on a number of graph-theoretic and algorithmic problems. There are several ways to model graphs geometrically and our main concern here is with geometric representations that respect the metric of the (possibly weighted) graph. Given a graph G we map its vertices to a normed space in an attempt to (i) Keep down the dimension of the host space and (ii) Guarantee a small distortion, i.e., make sure that distances between vertices in G closely match the distances between their geometric images. We develop efficient algorithms for embedding graphs low-dimensionally with a small distortion

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