On the Complexity of Multi-Round Divisible Load Scheduling

In this paper we study master-worker scheduling of divisible loads in heterogeneous distributed systems. Divisible loads are computations that can be arbitrarily divided into independent ``chunks'', which can then be processed in parallel. In multi-round scheduling load is sent to each worker as several chunks rather than as a single one. Solving the divisible load scheduling (DLS) problem entails determining the subset of workers that should be used, the sequence of communication to these workers, and the sizes of each load chunk. We first state and establish an optimality principle in the general case. Then we establish a new complexity result by showing that a DLS problem, whose complexity has been open for a long time, is in fact NP-hard, even in the one-round case. We also show that this problem is pseudopolynomially solvable under certain special conditions. Finally, we present a deep survey on algorithms and heuristics for solving the multi-round DLS problem.