Optimal performances and scheduling for parallel algorithms with equal cost tasks

Abstract

(PA) being a parallel algorithm involving n equal cost tasks, we study the P(τ) problem of determining the minimum required number of processors π to execute (PA) in minimum time τ regardless of communication costs. We use a binary search strategy based on a critical path oriented scheduling heuristic. O(n+m) to O([nlogn+m]logn) steps are required to compute a near optimal solution where m is the number of precedence constraints. A generalization to the problem P(t) (∀t>τ) and to the non equal cost tasks case is then easily introduced.