An R || C max Quantum Scheduling Algorithm

An R || C max Quantum Scheduling Algorithm Grover’s search algorithm can be applied to a wide range of problems; even problems not generally regarded as searching problems, can be reformulated to take advantage of quantum parallelism and entanglement, and lead to algorithms which show a square root speedup over their classical counterparts. In this paper, we discuss a systematic way to formulate such problems and give as an example a quantum scheduling algorithm for an R||Cmax problem. R||Cmax is representative for a class of scheduling problems whose goal is to find a schedule with the shortest completion time in an unrelated parallel machine environment. Given a deadline, or a range of deadlines, the algorithm presented in this paper allows us to determine if a solution to an R||Cmax problem with N jobs and M machines exists, and if so, it provides the schedule. The time complexity of the quantum scheduling algorithm is $${\mathcal{O}(\sqrt{M^N})}$$ while the complexity of its classical counterpart is $${\mathcal{O}(M^N)}$$ . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

An R || C max Quantum Scheduling Algorithm

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Publisher
Springer Journals
Copyright
Copyright © 2006 by Springer Science+Business Media, LLC
Subject
Physics; Characterization and Evaluation of Materials; Computer Science, general ; Engineering, general; Mathematics, general; Physics, general
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-006-0048-8
Publisher site
See Article on Publisher Site

Abstract

Grover’s search algorithm can be applied to a wide range of problems; even problems not generally regarded as searching problems, can be reformulated to take advantage of quantum parallelism and entanglement, and lead to algorithms which show a square root speedup over their classical counterparts. In this paper, we discuss a systematic way to formulate such problems and give as an example a quantum scheduling algorithm for an R||Cmax problem. R||Cmax is representative for a class of scheduling problems whose goal is to find a schedule with the shortest completion time in an unrelated parallel machine environment. Given a deadline, or a range of deadlines, the algorithm presented in this paper allows us to determine if a solution to an R||Cmax problem with N jobs and M machines exists, and if so, it provides the schedule. The time complexity of the quantum scheduling algorithm is $${\mathcal{O}(\sqrt{M^N})}$$ while the complexity of its classical counterpart is $${\mathcal{O}(M^N)}$$ .

Journal

Quantum Information ProcessingSpringer Journals

Published: Dec 12, 2006

References

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