A faster parallel algorithm for k-connectivity

Abstract

A new parallel algorithm for graph k-connectivity is shown. It runs in O( k log log k log n) time using ( n + k 2) k( C( n, m) + kn) processors on the ARBITRARY CRCW PRAM model, where C( n, m) is the number of processors required to compute the connected components in logarithmic time. The previous best algorithm runs in ( Ok 2 log n) time using ( n + k 2) kC( n, m) processors (Khuller et al., 1991). When k = log n for example, our new algorithm runs in time O( log 2 n log log log n) against O( log 3 n ) of Khuller's algorithm, i.e., almost an improvement of a factor of log n. The number of processors does not change (under the big-O notation) if m ⩾ kn log n, since C( n, m) is at least (m + n) log n . If we use ( n + k 2) k( C( n, m) + k 1 + ε n) processors, the bound can be further decreased to O( k log n).