We consider the special case of the two functions coarsest partitioning problem, where one of the functions is a cyclic permutation and the other arbitrary. Here we present a parallel algorithm on a CRCW PRAM that solves the above partitioning problem inO(α(n)log(β(n)))time usingO(n)processors, wherenis the set cardinality,β(n)is the number of distinct prime factors ofn,andα(n)is the sum of the exponents of the primes in the factorization ofn.In almost all cases the algorithm runs inO(loglognlogloglogn)time withnprocessors.