Online load balancing of temporary tasks
We consider non-preemptive online load balancing problem under the assumption that tasks have limited duration in time. Each task has to be assigned immediately upon arrival to one of the machines, increasing the load on this machine for the duration of the task. The goal is to minimize the maximum load.
Azar, Broder and Karlin studied the unknown duration case where for each task there is a subset of machines capable of executing it; the increase in load due to assignment of the task to one of these machines depends only on the task and not on the machine. For this case, they showed an O(n2/3)-competitive algorithm and an Ω(√n) lower bound, where n is the number of the machines. We close the gap by showing an O(√n)-competitive algorithm.
We also consider the related machines case with unknown task duration. Here, a task can be executed by any machine and the increase in load depends on the speed of the machine and the weight of the task. For this case we show a 20-competitive algorithm and a lower bound of 3−o(1).
Trying to overcome the Ω(√n) lower bound for the case of unknown task duration, we study a variant of the load balancing problem for tasks with known duration. For this case we show an O(log nT)-competitive algorithm, where T is the ratio of the maximum to minimum duration.
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- J. Aspenes, Y. Azar, A. Fiat, S. Plotkin, and O. Waarts. On-line machine scheduling with applications to load balancing and virtual circuit routing. In Proc. 23rd Annual ACM Symposium on Theory of Computing, May 1993.Google Scholar
- Y. Azar, A. Broder, and A. Karlin. On-line load balancing. In Proc. 33rd IEEE Annual Symposium on Foundations of Computer Science, pages 218–225, 1992.Google Scholar
- Y. Azar, J. Naor, and R. Rom. The competitiveness of on-line assignment. In Proc. 3rd ACM-SIAM Symposium on Discrete Algorithms, pages 203–210, 1992.Google Scholar
- Y. Bartal, A. Fiat, H. Karloff, and R. Vohra. New algorithms for an ancient scheduling problem. In Proc. 24th Annual ACM Symposium on Theory of Computing, 1992.Google Scholar
- R.L. Graham. Bounds for certain multiprocessing anomalies. Bell System Technical Journal, 45:1563–1581, 1966.Google Scholar
- T. Leighton, F. Makedon, S. Plotkin, C. Stein, É. Tardos, and S. Tragoudas. Fast approximation algorithms for multicommodity flow problem. In Proc. 23th ACM Symposium on the Theory of Computing, pages 101–111, May 1991.Google Scholar
- S. Plotkin, D. Shmoys, and É. Tardos. Fast approximation algorithms for fractional packing and covering problems. In Proc. 32nd IEEE Annual Symposium on Foundations of Computer Science, pages 495–504, October 1991.Google Scholar
- P. Raghavan and C.D. Thompson. Provably good routing in graphs: Regular arrays. In Proc. of 17th ACM Symp. on Theory of Computing, May 1985.Google Scholar
- D. Shmoys, J. Wein, and D.P. Williamson. Scheduling parallel machines online. In Proc. 32nd IEEE Annual Symposium on Foundations of Computer Science, pages 131–140, 1991.Google Scholar