Preemptive Scheduling of Equal-Length Jobs in Polynomial Time

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 wi Ci 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 n8 and hence, the problem is polynomially solvable for any fixed number k of different weights. Keywords Machine scheduling · Preemptive scheduling · Equal-length jobs · Parameterized algorithm · Polynomial algorithm Mathematics Subject Classification (2000) Primary 68M20; Secondary 90B35

• Type: Journal
• Year: 2010
• Where: MICS
• Authors: George B. Mertzios, Walter Unger
• Keywords: Algorithm, MICS 2010, Polynomial Algorithm Mathematics, Preemptive Scheduling Problem