Simple Algorithms for Gilmore–Gomory's Traveling Salesman and Related Problems
Journal of Scheduling
Complexity of Workforce Scheduling in Transfer Lines
Journal of Global Optimization
An approximation algorithm for a bottleneck traveling salesman problem
Journal of Discrete Algorithms
Power management using test-pattern ordering for wafer-level test during burn-in
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
The balanced traveling salesmanproblem
Computers and Operations Research
Complexity analysis of balloon drawing for rooted trees
Theoretical Computer Science
An approximation algorithm for a bottleneck traveling salesman problem
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Experimental analysis of heuristics for the bottleneck traveling salesman problem
Journal of Heuristics
A Hybrid Genetic Algorithm for the Bottleneck Traveling Salesman Problem
ACM Transactions on Embedded Computing Systems (TECS) - Special Issue on Modeling and Verification of Discrete Event Systems
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Consider the traveling salesman problem where the distance between two cities A and B is an integrable function of the y-coordinate of A and the x-coordinate of B. This problem finds important applications in operations management and combinatorial optimization. Gilmore and Gomory (Oper. Res. 12 (1964) 655) gave a polynomial time algorithm for this problem. In the bottleneck variant of this problem (BP), we seek a tour that minimizes the maximum distance between any two consecutive cities. For BP, Gilmore and Gomory state that they ''do not yet know how to solve the problem for general integrable functions''. We show that BP is strongly NP-complete. Also, we use this reduction to provide a method for proving NP-completeness of other combinatorial problems.