### Abstract:

We consider the classical on-line load balancing problem of temporary tasks under restricted assignments. Each job can be processed only on a subset of machines, different jobs require a different amounts of processing time, and once a job is assigned to a machine it cannot be reassigned to another machine. The on-line load balancing problem is to assign each job to an appropriate machine such that the maximum load on any machine at any point in time is minimized.
Online algorithms are usually analyzed using the competitive ratio, which is de ned as the ratio of the solution obtained by the online algorithm to that obtained by an offline adversary for the worst possible input sequence. The measure of analyzing online algorithms using the notion of a competitive ratio is too bleak. Two popular approaches that have been used to deal with a variety of objective functions in case of scheduling problems have been that of "resource augmentation" [4] and "rejection model" [5]. In this project, our aim is to extend the work of Choudhury et al. [5] to the temporary job settings. As an initial result, we analyze the standard greedy approach in rejection model without late rejections and arrive at the result that the competitive ratio for any on-line greedy algorithm is at-least
[(3m)2=3=4] and the upper bound for the same problem is [(3m)2=3=2](1+o(1)). Next,
we consider the same problem and arrive at the result that any online algorithm would have a competitive ratio at-least ( p 2m=2). At last, we consider the same problem but this time with late rejections allowed and show that lower bound for this problem is at-least (1=" 1) where " is the fraction of jobs which can be rejected.