Guaranteed performance heuristics for the bottleneck travelling salesman problem

Authors:
R.Gary Parker;Ronald L Rardin
Affiliations:
School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA;School of Industrial Engineering, Purdue University, W. Lafayette, IN 47907, USA
Venue:
Operations Research Letters
Year:
1984

Citing 3
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Abstract

We consider constant-performance, polynomial-time, nonexact algorithms for the minimax or bottleneck version of the Travelling Salesman Problem. It is first shown that no such algorithm can exist for problems with arbitrary costs unless P = NP. However, when costs are positive and satisfy the triangle inequality, we use results pertaining to the squares of biconnected graphs to produce a polynomial-time algorithm with worst-case bound 2 and show further that, unless P = NP, no polynomial alternative can improve on this value.