Executing Divisible Jobs on a Network with a Fixed Number of Processors

Abstract

In real practice, a job sometimes can be divided into s independent tasks to be distributed for execution on a network with a fixed number of processors. The overall finish time can vary widely depending on variables such as latency, data partitioning and/or data combining times, the individual execution times, the amount of data to be transferred, and the sending out of more tasks than needed. This paper studies the problem of finding an optimal task scheduling for a divisible job such that the overall finish time is minimized. We first prove the studied problem is NP-complete and give a simple 3-OPT approximation algorithm. Then we develop a (2 + ∈)-OPT linear-time approximation algorithm by generalizing our simple algorithm, where ∈ is an arbitrarily small constant. A linear-time 2-OPT approximation algorithm is given when we divide the tasks evenly. Algorithms to find optimal solutions are then given for two special cases: 1) when the network has exactly two processors and 2) when the evenly divided tasks have symmetric behaviors. These cases happen frequently in real practice.