The geometry of graphs and some of its algorithmic applications

Nathan Linial, Eran London, Yuri Rabinovich
1995 Combinatorica  
In this paper 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
more » ... tion, i.e., make sure that *Supported in part by grants from the Israeli Academy of Sciences, the Binational Science Foundation Israel-USA and the Niedersachsen-Isriel Research Program. in the practice of pattern-recognition, see Duda and Hart [15], especially chapter 6.
doi:10.1007/bf01200757 fatcat:lhkhob7abvhc7bhcfzyci7uqoy