Algorithms for minimizing maximum lateness with unit length tasks and resource constraints

AbstractThe problem we consider is that of scheduling n unit length tasks on identical processors in the presence of additional scarce resources. The objective is to minimize maximum lateness. It has been known for some time that the problem is NP-hard even for two processors and one resource type. In the present paper we show that the problem can be solved in O(n log n) time, even for an arbitrary number of resources if the instance of the problem has the saturation property (i.e., no resource unit is idle in an optimal schedule). For the more general problem without saturation, two heuristic algorithms and a branch and bound approach are proposed. The results of computational tests of the above methods are also reported

Scheduling a Divisible Task in a 2-Dimensional Toroidal Mesh

In this paper, a problem of scheduling an arbitrarily divisible task is considered. Taking into account both communication delays and computation time we propose a scheduling method which minimizes total execution time. We focus on two dimensional processor networks assuming a circuit-switching routing mechanism. The scheduling method uses a scattering scheme proposed in [15] to distribute parts of the task to processors in a minimum time. We show how to model and solve this problem with a set of algebraic equations. A solution of the latter allows one to analyze the performance of the network depending on various actual parameters of the task and the parallel machine. Though the method is de ned for a particular architecture and scattering scheme it can be generalized to analyze other architectures of parallel computer systems