Temporary tasks assignment resolved

Among all basic on-line load balancing problems, the only unresolved problem was load balancing of temporary tasks on unrelated machines. This open problem existed for almost a decade, see [12]. We resolve this problem by providing an inapproximability result. In addition, a newer open question is to identify the dependency of the competitive ratio on the durations of jobs in the case where durations are known. We resolve this problem by characterizing this dependency. Finally, we provide a PTAS for the off-line problem with a fixed number of machines and show a 2-inapproximability result for the general case.