Approximation Algorithms for Scheduling Independent Malleable Tasks  J. B la˙ zewicz, M. Machowiak 1 , G. Mouni´ e, and D. Trystram 2 1 Instytut Informatyki Politechnika Poznanska ul. Piotrowo 3a, 60 - 965 Poznan, Poland 2 ID-IMAG, 51 rue Jean Kuntzman 38330 Montbonnot Saint Martin, France Abstract. Malleable tasks consist in considering the tasks of a parallel program as large computational units that may be themselves paral- lelized. In this paper we investigate the problem of scheduling a set of n independent malleable tasks on a m processors system, starting from the continuous version of the problem. 1 Introduction The malleable task model is a recent model in parallel processing introduced in order to solve efficiently some practical problems [5,6,7]. These problems have complex behavior at the finest level of execution which brings classical methods of scheduling to their limits, mainly due to the explicit management of the com- munications. The idea of a malleable task (MT) results in solving the problem at a different level of granularity in order to globally take into account commu- nication costs and parallelization overheads with a simple penalty factor. Malleable tasks can be distinguished from multiprocessor tasks, considered for example in [1], where the number of processors allotted to each task is known. The latter model has received a considerable attention in the literature. The problem of scheduling independent MT without preemption (it means that each task is computed on a constant number of processors from its start to completion) is NP-hard [2], thus, an approximation algorithm with performance guarantee has been looked for. While the problem has an approximation scheme for any fixed value m, the number of processors, [4], no general practical polynomial approximation better than 2 is known [5]. In this paper starting from the continuous version of the problem (i.e. where the tasks may require a fractional part of the resources), we propose a different approximation algorithm with a performance guarantee equal to 2. Then, some improvements are derived.  This work was realized when J. Bla˙ zewicz was visiting ENSGI, Grenoble, in Spring 2000 and was partially supported by KBN Grant 8T11A01618 R. Sakellariou et al. (Eds.): Euro-Par 2001, LNCS 2150, pp. 191–197, 2001. c  Springer-Verlag Berlin Heidelberg 2001