We present a new optimal construction of semi-separated pair
decomposition (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, we
present a new construction of a \tspanner with O(n) edges and
maximum degree O( log2 n) that has a separator of
size O(n1-1/d).