Optimal scheduling for two-processor systems

@article{Coffman2004OptimalSF,
  title={Optimal scheduling for two-processor systems},
  author={Edward G. Coffman and Ronald L. Graham},
  journal={Acta Informatica},
  year={2004},
  volume={1},
  pages={200-213}
}
SummaryDespite the recognized potential of multiprocessing little is known concerning the general problem of finding efficient algorithms which compute minimallength schedules for given computations and m≧2 processors. In this paper we formulate a general model of computation structures and exhibit an efficient algorithm for finding optimal nonpreemptive schedules for these structures on two-processor systems. We prove that the algorithm gives optimal solutions and discuss its application to… 
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References

SHOWING 1-10 OF 12 REFERENCES
Optimal Preemptive Scheduling on Two-Processor Systems
TLDR
This paper considers the static scheduling of computations for a system containing two indentical processors and a solution for the two-machine case with preemptive scheduling is presented.
Optimal Sequencing of Two Equivalent Processors
This paper presents an efficient algorithm for a class of sequencing problems in which n tasks with an arbitrary precedence relation have to be processed by two processors of equal ability, and each
Parallel Sequencing and Assembly Line Problems
TLDR
This paper deals with a new sequencing problem in which n jobs with ordering restrictions have to be done by men of equal ability, and how to arrange a schedule that requires the minimum number of men to complete all jobs within a prescribed time T.
Bounds for certain multiprocessing anomalies
It is known that in multiprocessing systems composed of many identical processing units operating in parallel, certain timing anomalies may occur; e.g., an increase in the number of processing units
Paths, Trees, and Flowers
A graph G for purposes here is a finite set of elements called vertices and a finite set of elements called edges such that each edge meets exactly two vertices, called the end-points of the edge. An
SCHEDULING IN PROJECT NETWORKS
TLDR
Three scheduling problems that involve a schedule or timetable of projected operations or jobs occur frequently in operations research and each poses a question about a finite partially ordered set of jobs that can be reformulated in terms of flows in acyclic directed networks.
Scheduling project networks
I t has been found useful to describe a project, a series of interrelated activities or procedures directed toward the accomplishment of some definable goal, by a network of nodes and directed line
The Gantt Chart
...
...