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 weights

[1]  Peter Brucker,et al.  Scheduling Algorithms , 1995 .

[2]  Joseph Y.-T. Leung,et al.  Preemptive Scheduling to Minimize Mean Weighted Flow Time , 1990, Inf. Process. Lett..

[3]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[4]  Joseph Y.-T. Leung,et al.  Preemptive Scheduling of Equal Length Jobs on Two Machines to Minimize Mean Flow Time , 1990, Oper. Res..

[5]  A. J. Clewett,et al.  Introduction to sequencing and scheduling , 1974 .

[6]  B. J. Lageweg,et al.  Scheduling identical jobs on uniform parallel machines , 1989 .

[7]  Robert E. Tarjan,et al.  Scheduling Unit-Time Tasks with Arbitrary Release Times and Deadlines , 1981, SIAM J. Comput..

[8]  Nodari Vakhania,et al.  Preemptive scheduling of equal-length jobs to maximize weighted throughput , 2002, Oper. Res. Lett..

[9]  Philippe Baptiste,et al.  Scheduling equal-length jobs on identical parallel machines , 2000, Discret. Appl. Math..

[10]  Marek Chrobak,et al.  The complexity of mean flow time scheduling problems with release times , 2006, J. Sched..

[11]  Barbara B. Simons,et al.  Multiprocessor Scheduling of Unit-Time Jobs with Arbitrary Release Times and Deadlines , 1983, SIAM J. Comput..

[12]  Eugene L. Lawler,et al.  Preemptive scheduling of uniform machines subject to release dates : (preprint) , 1979 .

[13]  T. C. Edwin Cheng,et al.  An O(n2) algorithm for scheduling equal-length preemptive jobs on a single machine to minimize total tardiness , 2006, J. Sched..

[14]  Philippe Baptiste,et al.  An O(n4) algorithm for preemptive scheduling of a single machine to minimize the number of late jobs , 1999, Oper. Res. Lett..

[15]  E. L. Lawler,et al.  A dynamic programming algorithm for preemptive scheduling of a single machine to minimize the number of late jobs , 1991 .

[16]  Jan Karel Lenstra,et al.  Complexity of machine scheduling problems , 1975 .