Scheduling independent jobs for torus connected networks with/without link contention

In this paper, we investigate the problem of how to schedule n independent jobs on an m × m torus based network. We develop a model to to quantify the effect of contention for communication links on the dilation of job execution time when multiple jobs share communication links; we then design an efficient algorithm to schedule a set of n independent jobs with different torus size requirements on a given torus with an objective to minimize the total schedule length. We also develop a feasibility algorithm for pre-emptively scheduling a given set of jobs on a torus of given size with a given deadline. We provide analysis for both the algorithms.