Aiming to optimize job scheduling in computer systems, this paper tackles the NP-hard problem of scheduling independent jobs in partitionable mesh connected systems. It analyzes a simple approximation algorithm, Am, showing that under certain conditions, the average-case performance ratio E(Am(L))/E(OPT(L)) is asymptotically bounded from above by 1.6637594.... The algorithm’s efficiency is particularly pronounced when jobs request square submeshes or smaller submeshes. The analysis assumes that the sizes of submeshes requested by jobs are independent and identically distributed (i.i.d.) random variables uniformly distributed within specific ranges, with task execution times also being i.i.d. random variables with finite mean and variance. This research contributes to the development of more efficient job scheduling algorithms in parallel computing environments, which may improve performance in various *computer science* applications. These findings are valuable for optimizing resource allocation in *computer* systems.
Published in the International Journal of Foundations of Computer Science, this paper fits directly within the journal's focus on theoretical computer science and algorithmic design. The analysis of a job scheduling algorithm in partitionable mesh connected systems contributes to the ongoing research on efficient resource allocation and optimization, which is of significant interest to the journal's readership. The mathematical analysis and algorithmic design provide valuable insights for improving computer system performance.