New constructions of SSPDs and their applications

We present a new optimal construction of a semi-separated pair decomposition (i.e., SSPD) for a set of n points in ^Rd. In the new construction each point participates in a few pairs, and it extends easily to spaces with low doubling dimension. This is the first optimal construction with these properties. As an application of the new construction, for a fixed t>1, we present a new construction of a t-spanner with O(n) edges and maximum degree O( ^log2n) that has a separator of size O(n1 ^-1/d).