On-Line Load Balancing of Temporary Tasks

This paper considers the nonpreemptive on-line load balancing problem where tasks havelimited durationin time. Upon arrival, each task has to be immediately assigned to one of the machines, increasing the load on this machine for the duration of the task by an amount that depends on both the machine and the task. The goal is to minimize the maximum load. Azar, Broder, and Karlin studied theunknown durationcase where the duration of a task is not known upon its arrival (On-line load balancingin“Proc. 33rd IEEE Annual Symposium on Foundations of Computer Science, 1992,” pp. 218Â?225). They focused on the special case in which for each task there is a subset of machines capable of executing it, and the increase in load due to assigning the task to one of these machines depends only on the task and not on the machine. For this case, they showed anO(n2/3)- competitive algorithm, and anÂ?(n)lower bound on the competitive ratio, wherenis the number of the machines. This paper closes the gap by giving anO(n)-competitive algorithm. In addition, trying to overcome theÂ?(n)lower bound for the case of unknown task duration, this paper initiates a study of the load balancing problem for tasks withknown duration(i.e., the duration of a task becomes known upon its arrival). For this case we show anO(lognT)-competitive algorithm, whereTis the ratio of the maximum possible duration of a task to the minimum possible duration of a task. The paper explores an alternative way to overcome theÂ?(n)bound; it considers therelated machinescase with unknown task duration. In the related machines case, 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 the paper gives a 20-competitive algorithm and shows a lower bound of 3Â?o(1) on the competitive ratio.