Dynamic Scheduling on Parallel Machines

Anja Feldmann, Jirí Sgall, Shang-Hua Teng

Abstract: We study the problem of on-line job-scheduling on parallel machines with different network topologies. An on-line scheduling algorithm schedules a collection of parallel jobs with known resource requirements but unknown running times on a parallel machine.We give an O(log log N)<math><mtext>O(</mtext><mtext>log log N</mtext><mtext>)</mtext></math>-competitive algorithm for on-line scheduling on a two-dimensional mesh of N processors and we prove a matching lower bound of Ω(log log N)<math><mtext>Ω(</mtext><mtext>log log N</mtext><mtext>)</mtext></math> on the competitive ratio. Furthermore, we show tight constant bounds of 2 for PRAMs and hypercubes, and present a 2.5-competitive algorithm for lines. We also generalize our two-dimensional mesh result to higher dimensions. Surprisingly, our algorithms become less and less greedy as the geometric structure of the network topology becomes more complicated. The proof of our lower bound for the two- dimensional mesh actually shows that no greedy-like algorithm can perform well.