ONLINE SCHEDULING OF DYNAMIC TREES
Michael A. Palis, Jing-Chiou Liou, Sanguthevar Rajasekaran, Sunil M. Shende, David S. L. Wei · Parallel Processing Letters · 1995
The scheduling problem for dynamic tree-structured task graphs is studied and is shown to be inherently more difficult than the static case. It is shown that any online scheduling algorithm, deterministic or randomized, has competitive ratio Ω((1/g)/ log d (1/g)) for trees with granularity g and degree at most d. On the other hand, it is known that static trees with arbitrary granularity can be scheduled to within twice the optimal schedule. It is also shown that the lower bound is tight: there is a deterministic online tree scheduling algorithm that has competitive ratio O((1/g)/ log d (1/g)). Thus, randomization does not help.