Task scheduling with restricted preemptions

One of basic problems in task scheduling is finding the shortest schedule for a given set of tasks. In this paper we analyze a restricted version of the general preemptive scheduling problem, where tasks can only be divided into parts at least as long as a given parameter k. We introduce a heuristic scheduling method TSRP3. Number of processors m, number of tasks n and task lengths p_i are assumed to be known. If n ≥ 2m and k is sufficiently small, TSRP3 finds shortest possible schedule with O(m) divisions in polynomial time. In addition we introduce a more robust algorithm TSRP4 based on combining TSRP3 with multi-fit.