Preemptive Scheduling of Equal-Length Jobs in Polynomial Time

摘要

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 ∑_(i=1)~n w_iC_i 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)~k n~8) and hence, the problem is polynomially solvable for any fixed number k of different weights.