Optimal and online preemptive scheduling on uniformly related machines. ITI Series 2003-171

We consider the problem of preemptive scheduling on uniformly related machines.We present a semi-online algorithm which, if the optimal makespan is given in advance, produces an optimal schedule. Using the standard doubling technique, this yields a 4 competitive deterministic and 2.71 competitive randomized online algorithms. In addition, it matches the performance of the previously.....

A note on semi-online machine covering

In the machine cover problem we are given m machines and n jobs to be assigned (scheduled) so that the smallest load of a machine is as large as possible. A semi-online algorithm is given in advance the optimal value of the smallest load for the given instance, and then the jobs are scheduled one by one as they arrive, without any knowledge of the following jobs.We present a deterministic algorithm with competitive ratio 11/6 = 1.834 for machine covering with any number of machines and a lower bound showing that no deterministic algorithm can have a competitive ratio below 43/24 = 1.791

A note on semi-online machine covering

In the machine cover problem we are given m machines and n jobs to be assigned (scheduled) so that the smallest load of a machine is as large as possible. A semi-online algorithm is given in advance the optimal value of the smallest load for the given instance, and then the jobs are scheduled one by one as they arrive, without any knowledge of the following jobs.We present a deterministic algorithm with competitive ratio 11/6 = 1.834 for machine covering with any number of machines and a lower bound showing that no deterministic algorithm can have a competitive ratio below 43/24 = 1.791

A note on semi-online machine covering

In the machine cover problem we are given m machines and n jobs to be assigned (scheduled) so that the smallest load of a machine is as large as possible. A semi-online algorithm is given in advance the optimal value of the smallest load for the given instance, and then the jobs are scheduled one by one as they arrive, without any knowledge of the following jobs.We present a deterministic algorithm with competitive ratio 11/6 = 1.834 for machine covering with any number of machines and a lower bound showing that no deterministic algorithm can have a competitive ratio below 43/24 = 1.791

Better Algorithms for Online Bin Stretching

Online Bin Stretching is a semi-online variant of bin packing in which the algorithm has to use the same number of bins as the optimal packing, but is allowed to slightly overpack the bins. The goal is to minimize the amount of overpacking, i.e., the maximum size packed into any bin. We give an algorithm for Online Bin Stretching with a stretching factor of 1:5 for any number of bins. We also show a specialized algorithm for three bins with a stretching factor of 11=8 = 1:375