Makespan minimization in job shops: a polynomial time approximation scheme
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Better approximation guarantees for job-shop scheduling
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Approximating Scheduling Unrelated Parallel Machines in Parallel
Computational Optimization and Applications
Polynomial Time Approximation Schemes for the Multiprocessor Open and Flow Shop Scheduling Problem
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
A Randomized Algorithm for Flow Shop Scheduling
Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science
Convergence Analysis of Simulated Annealing-Based Algorithms Solving Flow Shop Scheduling Problems
CIAC '00 Proceedings of the 4th Italian Conference on Algorithms and Complexity
On scheduling in map-reduce and flow-shops
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
Joint optimization of overlapping phases in MapReduce
Performance Evaluation
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Shop scheduling problems are notorious for their intractability, both in theory and practice. In this paper, we demonstrate the existence of a polynomial approximation scheme for the flow shop scheduling problem with an arbitrary fixed number of machines. For the three common shop models (open, flow, and job), this result is the only known approximation scheme. Since none of the three models can be approximated arbitrarily closely in the general case (unless P=NP), the result demonstrates the approximability gap between the models in which the number of machines is fixed, and those in which it is part of the input of the instance. The result can be extended to flow shops with job release dates and delivery times and to flow shops with a fixed number stages, where the number of machines at any stage is fixed. We also describe a related polynomial approximation scheme for the problem of scheduling an open shop with a single bottleneck machine and an arbitrary number of non-bottleneck machines.