An algorithm for solving the job-shop problem
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Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
A fast quantum mechanical algorithm for database search
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Strengths and Weaknesses of Quantum Computing
SIAM Journal on Computing
Scheduling Unrelated Machines by Randomized Rounding
SIAM Journal on Discrete Mathematics
Unrelated parallel machine scheduling with resource dependent processing times
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
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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 $${\mathcal{O}(M^N)}$$ .