Optimal preemptive semi-online scheduling on two uniform processors

We investigate a preemptive semi-online scheduling problem. Jobs with sizes within a certain range [1, r] (r≥1 ) arrive one by one to be scheduled on two uniform parallel processors with speed 1 and s≥1, respectively. The objective is to minimize makespan. We characterize the optimal competitive ratio as a function of both s and r by devising a deterministic on-line scheduling algorithm along with a matching lower bound, which also holds for randomized algorithms.

[1]  Zsolt Tuza,et al.  Semi-On-line Scheduling on Two Parallel Processors with an Upper Bound on the Items , 2003, Algorithmica.

[2]  Eugene L. Lawler,et al.  Sequencing and scheduling: algorithms and complexity , 1989 .

[3]  Donglei Du,et al.  Preemptive on-line scheduling for two uniform processors , 1998, Oper. Res. Lett..

[4]  Gerhard J. Woeginger,et al.  Semi-online scheduling with decreasing job sizes , 2000, Oper. Res. Lett..

[5]  Jeffrey B. Sidney,et al.  Ordinal algorithms for parallel machine scheduling , 1996, Oper. Res. Lett..

[6]  Leah Epstein,et al.  Optimal non-preemptive semi-online scheduling on two related machines , 2005, J. Algorithms.

[7]  Gerhard J. Woeginger,et al.  Randomized online scheduling on two uniform machines , 2001, SODA '99.

[8]  Gerhard J. Woeginger,et al.  An Optimal Algorithm for Preemptive On-line Scheduling , 1994, ESA.

[9]  Leah Epstein,et al.  Optimal preemptive semi-online scheduling to minimize makespan on two related machines , 2002, Oper. Res. Lett..

[10]  Graham K. Rand,et al.  Logistics of Production and Inventory , 1995 .

[11]  Zsolt Tuza,et al.  Semi on-line algorithms for the partition problem , 1997, Oper. Res. Lett..

[12]  Guochuan Zhang,et al.  Semi On-Line Scheduling on Two Identical Machines , 1999, Computing.

[13]  Donglei Du,et al.  Randomized On-Line Scheduling Similar Jobs to Minimize Makespan on Two Identical Processors , 2005 .

[14]  Teofilo F. Gonzalez,et al.  Preemptive Scheduling of Uniform Processor Systems , 1978, JACM.