Minimizing the flow time without migration

We consider the classical problem of scheduling jobs in a multiprocessor setting in order to minimize the flow time (total time in the system). The performance of the algorithm, both in offline and online settings, can be significantly improved if we allow preemption, i.e., interrupt a job and later continue its execution, perhaps migrating it to a different machine. Preemption is inherent to make a scheduling algorithm efficient. While in the case of a single processor most operating systems can easily handle preemptions, migrating a job to a different machine results in a huge overhead. Thus, it is not commonly used in most multiprocessor operating systems. The natural question is whether migration is an inherent component for an efficient scheduling algorithm in either the online or offline setting. Leonardi and Raz [Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, El Paso, TX, 1997, pp. 110-119] showed that the well-known algorithm, shortest remaining processing time (SRPT), performs within a logarithmic factor of the optimal offline algorithm. Note that SRPT must use both preemption and migration to schedule the jobs. It is not known if better approximation factors can be reached and thus SRPT, although it is an online algorithm, becomes the best known algorithm in the offline setting. In fact, in the online setting, Leonardi and Raz showed that no algorithm can achieve a better bound. Without migration, no (offline or online) approximations are known. This paper introduces a new algorithm that does not use migration, works online, and is just as effective (in terms of approximation ratio) as the best known offline algorithm that uses migration.