B Veltman

Preemptive scheduling in a two-stage multiprocessor flow shop is NP-hard

In 1954, Johnson gave an efficient algorithm for minimizing makespan in a two-machine flow shop; there is no advantage to preemption in this case. McNaughtons wrap-around rule of 1959 finds a shortest preemptive schedule on identical parallel machines in linear time. A similarly efficient algorithm is unlikely to exist for the simplest common generalization of these problems. We show that preemptive scheduling in a two-stage flow shop with at least two identical parallel machines in one of the stages so as to minimize makespan is NP-hard in the strong sense.

Multiprocessor scheduling with communication delays

This paper adresses certain types of scheduling problems that arise when a parallel computation is to be executed on a multiprocessor. We define a model that allows for communication delays between precedence-related tasks, and propose a classification of various submodels. We also review complexity results and optimization and approximation algorithms that have been presented in the literature.

Complexity of scheduling multiprocessor tasks with prespecified processor allocations

We investigate the computational complexity of scheduling multiprocessor tasks with prespecified processor allocations. We consider two criteria: minimizing schedule length and minimizing the sum of the task completion times. In addition, we investigate the complexity of problems when precedence constraints or release dates are involved.

The Complexity of Scheduling Trees with Communication Delays

We consider the problem of finding a minimum-length schedule onmmachines for a set ofnunit-length tasks with a forest of intrees as precedence relation, and with unit interprocessor communication delays. First, we prove that this problem is NP-complete; second, we derive a linear time algorithm for the special case thatmequals 2.

The complexity of scheduling trees with communication delays

We consider the problem of finding a minimum-length schedule on m machines for a set of n unit-length tasks with a forest of intrees as precedence relation, and with unit interprocessor communication delays. First we prove that this problem is NP-complete; second we derive a linear time algorithm for the special case that m equals 2.