Scheduling unit-time tasks with limited resources
A set of tasks are to be scheduled on a multiprocessing system with s resources. Each task takes one unit time to complete, and requires certain amounts of resources. The schedule is to be consistent with a prescribed partial order relation on the task, and the total demand for each resource must not exceed a fixed amount at any instant. In this paper we analyze the worst-case behavior of several heuristic scheduling algorithms.
Let ω be the time taken for executing all the tasks according to a priority list, and ω0 be the time required when scheduled in an optimal way. It is shown that, independent of the number of processors, ω/ω0 ≦ sω0/2 + 0(s) for any list. When certain heuristic algorithms are used to prepare the list, a significantly improved upper bound can be derived: ω/ω0 ≦ const. × s + 0(1). Some generalizations are possible to the case when the "unit-time" restriction is removed.
When the partial order relation is empty, the problem becomes a natural generalization of the bin-packing problem. Tighter bounds for this special situation are given.
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