Constructing sparse t-spanners with small separators

Abstract

Given a set of n points S in the plane and a real value t > 1 we show how to construct in time script O sign(n log n) a t-spanner G of S such that there exists a set of vertices S′ of size script O sign(√/n log n) whose removal leaves two disconnected sets A and B where neither is of size greater than 2/3 · n. The spanner also has some additional properties; low weight and constant degree. © Springer-Verlag Berlin Heidelberg 2003.