A parameterized algorithm for the preemptive scheduling of equal-length jobs.

We study the preemptive scheduling problem of a set of n jobs with release times and equal processing times on a single machine. The objective is to minimize the sum of the weighted completion times n i=1 wiCi of the jobs. We propose for this problem the first parameterized algorithm on the number k of different weights. The runtime of the proposed algorithm is O((n k +1)kn8) and hence, this is the first polynomial algorithm for any fixed number k of different weight