Dynamic scheduling on parallel

Feldmann, A., J. Sgall and S.-H. Teng, Dynamic scheduling on parallel machines, Theoretical Computer Science 130 (1994) 49-72. 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(dm)-competitive algorithm for on-line scheduling on a two-dimensional mesh of N processors and we prove a matching lower bound of a( log log N) 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 twodimensional mesh actually shows that no greedy-like algorithm can perform well.