Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
The competitiveness of on-line assignments
Journal of Algorithms
On-line routing of virtual circuits with applications to load balancing and machine scheduling
Journal of the ACM (JACM)
A lower bound for randomized on-line multiprocessor scheduling
Information Processing Letters
Approximation schemes for scheduling
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Preemptive Scheduling of Real-Time Tasks on Multiprocessor Systems
Journal of the ACM (JACM)
A Level Algorithm for Preemptive Scheduling
Journal of the ACM (JACM)
Preemptive Scheduling of Uniform Processor Systems
Journal of the ACM (JACM)
On Preemptive Scheduling of Unrelated Parallel Processors by Linear Programming
Journal of the ACM (JACM)
On-line load balancing for related machines
Journal of Algorithms
Optimal scheduling of independent tasks on heterogeneous computing systems
ACM '74 Proceedings of the 1974 annual conference - Volume 1
Optimal Preemptive Scheduling on Two-Processor Systems
IEEE Transactions on Computers
The Power of Reordering for Online Minimum Makespan Scheduling
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
A robust APTAS for the classical bin packing problem
Mathematical Programming: Series A and B
Online Scheduling with Bounded Migration
Mathematics of Operations Research
The Power of Preemption on Unrelated Machines and Applications to Scheduling Orders
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Optimal and online preemptive scheduling on uniformly related machines
Journal of Scheduling
Optimal preemptive scheduling for general target functions
Journal of Computer and System Sciences
A robust PTAS for machine covering and packing
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
AFPTAS Results for Common Variants of Bin Packing: A New Method for Handling the Small Items
SIAM Journal on Optimization
Preemptive Online Scheduling with Reordering
SIAM Journal on Discrete Mathematics
A lower bound for on-line scheduling on uniformly related machines
Operations Research Letters
Preemptive on-line scheduling for two uniform processors
Operations Research Letters
An optimal algorithm for preemptive on-line scheduling
Operations Research Letters
Optimal preemptive on-line scheduling on uniform processors with non-decreasing speed ratios
Operations Research Letters
The power of deferral: maintaining a constant-competitive steiner tree online
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
A robust AFPTAS for online bin packing with polynomial migration,
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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Preemptive scheduling problems on parallel machines are classic problems. Given the goal of minimizing the makespan, they are polynomially solvable even for the most general model of unrelated machines. In these problems, a set of jobs is to be assigned to be executed on a set of m machines. A job can be split into parts arbitrarily and these parts are to be assigned to time slots on the machines without parallelism, that is, for every job, at most one of its parts can be processed at each time. Motivated by sensitivity analysis and online algorithms, we investigate the problem of designing robust algorithms for constructing preemptive schedules. Robust algorithms receive one piece of input at a time. They may change a small portion of the solution as an additional part of the input is revealed. The capacity of change is based on the size of the new input. For scheduling problems, the maximum ratio between the total size of the jobs (or parts of jobs) which may be re-scheduled upon the arrival of a new job j, and the size of j, is called migration factor. We design a strongly optimal algorithm with the migration factor 1- 1/m for identical machines. Such algorithms avoid idle time and create solutions where the (non-increasingly) sorted vector of completion times of the machines is minimal lexicographically. In the case of identical machines this results not only in makespan minimization, but the created solution is also optimal with respect to any lp norm (for p 1). We show that an algorithm of a smaller migration factor cannot be optimal with respect to makespan or any other norm, thus the result is best possible in this sense as well. We further show that neither uniformly related machines nor identical machines with restricted assignment admit an optimal algorithm with a constant migration factor. This lower bound holds both for makespan minimization and for any lp norm. Finally, we analyze the case of two machines and show that in this case it is still possible to maintain an optimal schedule with a small migration factor in the cases of two uniformly related machines and two identical machines with restricted assignment.