Given a connected graph G = (V; E) with n vertices and m edges, the
distance between two vertices in G is the weight of the shortest path between
them. A subgraph G0 is a t-spanner (an approximate t-spanner) of G if, for every
u, v 2 V , the distance between u and v in G0 is at most t (f(t)) times longer
than the distance in G, where f(t) is a polynomial function of variable t and t <=
f(t) < n. In this paper parallel algorithms for finding approximate t-spanners
on both unweighted graphs and weighted graphs are given. If G is an unweighted
graph, our algorithm requires O( ntk log n) time and M(n) processors, and the
spanner generated has size of O(( ntk )1+1=t +n) and factor of O(tk+1); otherwise
our algorithm requires O(( ntk )2 +( ntk )1+2=(t?2) log n) time and O(n2) processors,