Online Scheduling of Parallel Jobs on Hypercubes: Maximizing the Throughput

Abstract

Abstract. We study the online problem of scheduling unit-time parallel jobs on hypercubes. A parallel job has to be scheduled between its release time and deadline on a subcube of processors. The objective is to maximize the number of early jobs. We provide a 1.6-competitive algorithm for the problem and prove that no deterministic algorithm is better than 1.4-competitive.

Analysis on the computability over the efficient utilization problem of the four-dimensional space-time

“…We can greatly enhance the flexibility of how to utilize the space and time, and improve the container's space-time utilization ratio by this new model. Its applications include the manufacturing process in large-scale factories, the memory space allocation on computers, the parallel task scheduling on hypercubes [8], etc. In accordance with this new model, we presented an intuitive instance of baking biscuits [9], in which the entire working time of the oven was saved by a third.…”

“…8, so there must exist a global minimum point p * for U defined on H . k can no longer have smaller values independently and feasibly, or else it would be contradict with the conclusion that p * is a global minimum point for the potential energy U .…”