# Online load balancing of temporary tasks

## Abstract

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(n*^{2/3})-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.

## Keywords

Competitive Ratio## Preview

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