Shared processor scheduling

We study the shared processor scheduling problem with a single shared processor where a unit time saving (weight) obtained by processing a job on the shared processor depends on the job. A polynomialtime optimization algorithm has been given for the problem with equal weights in the literature. This paper extends that result by showing an O(n log n) optimization algorithm for a class of instances in which non-decreasing order of jobs with respect to processing times provides a non-increasing order with respect to weights — this instance generalizes the unweighted case of the problem. This algorithm also leads to a 2 -approximation algorithm for the general weighted problem. The complexity of the weighted problem remains open.