Parallelization of the critical path algorithm for a parallel computer

In this paper we consider parallelisation on a parallel computer with shared memory of the critical path algorithm for 2-steps graph with constant task cost. This graph occures in the parallelisation of block triangular linear system resolution. We present the parallel execution time including the communication cost of the critical path algorithm, and rue theoretically and practically determine the optimal ,value of the black site which minimises the parallel execution time.