A heuristic with worst-case analysis for minimax routing of two travelling salesmen on a tree. (English) Zbl 0848.90117
Summary: Suppose two tavelling salesmen must visit together all points/nodes of a tree, and the objective is to minimize the maximal length of their tours. Home locations of the salesmen are given, and it is required to find optimal tours. For this NP-hard problem a heuristic with complexity \(O(n)\) is presented. The worst-case relative error for the heuristic performance is \({1\over 3}\) for the case of equal home locations for both servers and \({1\over 2}\) for the case of different home locations.
MSC:
| 90C35 | Programming involving graphs or networks |
References:
| [1] | Frederickson, G. N.; Hecht, M. S.; Kim, C. E., Approximation algorithms for some routing problems, SIAM J. Comput., 7, 178-193 (1978) |
| [2] | Garey, M.; Johnson, D., Computers and Intractability (1979), Freeman: Freeman San Francisco · Zbl 0411.68039 |
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