Spanning ratios for a class of generalized Delaunay graphs

Kerry Cerqueira

Carleton University

In this talk we will discuss how a fundamental notion of operator algebras, the operator norm, can be used in a simple way to shed some light on the computation of spanning ratios for generalized Delaunay graphs. Some specific examples will be covered, which represent (we think) the best known current bounds for those networks. We will continue to discuss how the operator norm and the spanning ratio of a network can be discussed in less constrained settings with different norms, and here too, the geometric theory of Banach spaces yields some easy insights.