The Three-Machine No-Wait Flow Shop is NP-Complete
Journal of the ACM (JACM)
Flowshop scheduling with limited temporary storage
Journal of the ACM (JACM)
Makespan Minimization in No-Wait Flow Shops: A Polynomial Time Approximation Scheme
SIAM Journal on Discrete Mathematics
Approximation algorithms for asymmetric TSP by decomposing directed regular multigraphs
Journal of the ACM (JACM)
A new approximation algorithm for the asymmetric TSP with triangle inequality
ACM Transactions on Algorithms (TALG)
Improved Approximation Ratios for Traveling Salesperson Tours and Paths in Directed Graphs
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
An O(log n/ log log n)-approximation algorithm for the asymmetric traveling salesman problem
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
The Design of Approximation Algorithms
The Design of Approximation Algorithms
Operations Research Letters
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In this paper we study the classical no-wait flowshop scheduling problem with makespan objective (F|no−wait|Cmax in the standard three-field notation). This problem is well-known to be a special case of the asymmetric traveling salesman problem (ATSP) and as such has an approximation algorithm with logarithmic performance guarantee. In this work we show a reverse connection, we show that any polynomial time α-approximation algorithm for the no-wait flowshop scheduling problem with makespan objective implies the existence of a polynomial-time α(1+ε)-approximation algorithm for the ATSP, for any ε0. This in turn implies that all non-approximability results for the ATSP (current or future) will carry over to its special case. In particular, it follows that no-wait flowshop problem is APX-hard, which is the first non-approximability result for this problem.