Online hierarchical scheduling on two machines with known total size of low-hierarchy jobs

In this paper, we consider three versions of semi-online hierarchical scheduling problems on two identical machines, with the purpose of minimizing the makespan. In the first version, we assume that the total size of jobs with lower hierarchy is given and we get the tight bound . In the second one, assume that the total size of jobs in each hierarchy is given and we get the tight bound . In the third one, we assume that the total size of jobs with lower hierarchy is known in advance and a buffer of size K is given to store at most K jobs temporarily. We propose an optimal algorithm with competitive ratio using K=1 and show that a bigger buffer size is not helpful.

[1]  Jing Liu,et al.  Optimal semi-online algorithms for scheduling problems with reassignment on two identical machines , 2011, Inf. Process. Lett..

[2]  Joseph Y.-T. Leung,et al.  Makespan minimization in online scheduling with machine eligibility , 2013, Ann. Oper. Res..

[3]  Kangbok Lee,et al.  Online and semi-online scheduling of two machines under a grade of service provision , 2006, Oper. Res. Lett..

[4]  Yong Wu,et al.  Optimal Semi-online Scheduling Algorithms on Two Parallel Identical Machines under a Grade of Service Provision , 2010, AAIM.

[5]  Guochuan Zhang,et al.  A Simple Semi On-Line Algorithm for P2//C_{max} with a Buffer , 1997, Inf. Process. Lett..

[6]  T. C. Edwin Cheng,et al.  An FPTAS for parallel-machine scheduling under a grade of service provision to minimize makespan , 2008, Inf. Process. Lett..

[7]  Leah Epstein,et al.  Bin stretching revisited , 2003, Acta Informatica.

[8]  Yong He,et al.  Semi-on-line problems on two identical machines with combined partial information , 2002, Oper. Res. Lett..

[9]  Kangbok Lee,et al.  Semi-online scheduling with GoS eligibility constraints , 2014 .

[10]  He Yong,et al.  Optimal online algorithms for scheduling on two identical machines under a grade of service , 2006 .

[11]  Yiwei Jiang,et al.  Online scheduling on parallel machines with two GoS levels , 2006, J. Comb. Optim..

[12]  Gerhard J. Woeginger.  A comment on parallel-machine scheduling under a grade of service provision to minimize makespan , 2009, Inf. Process. Lett..

[13]  Haina Sun,et al.  Semi-online Multiprocessor Scheduling with Nonsimultaneous Machine Available Times , 2010, 2010 Third International Conference on Information and Computing.

[14]  Joseph Naor,et al.  On-Line Load Balancing in a Hierarchical Server Topology , 2002, SIAM J. Comput..

[15]  Yong He,et al.  Semi-Online Algorithms for Parallel Machine Scheduling Problems , 2003, Computing.

[16]  Xin Chen,et al.  Semi-online hierarchical scheduling problems with buffer or rearrangements , 2013, Inf. Process. Lett..

[17]  Zhiyi Tan,et al.  A note on hierarchical scheduling on two uniform machines , 2010, J. Comb. Optim..

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

[19]  Guochuan Zhang,et al.  A note on on-line scheduling with partial information , 2002 .

[20]  Kangbok Lee,et al.  Improved bounds for online scheduling with eligibility constraints , 2011, Theor. Comput. Sci..

[21]  Kangbok Lee,et al.  Semi-online scheduling problems on a small number of machines , 2013, J. Sched..

[22]  Ronald L. Graham,et al.  Bounds for certain multiprocessing anomalies , 1966 .

[23]  Kangbok Lee,et al.  Parallel machine scheduling under a grade of service provision , 2004, Comput. Oper. Res..