Guaranteed performance heuristics for the bottleneck travelling salesman problem

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.