zbMATH — the first resource for mathematics

\((p-1)/(p+1)\)-approximate algorithms for \(p\)-traveling salesmen problems on a tree with minmax objective. (English) Zbl 0879.68077
Summary: Suppose \(p\) traveling salesman must visit together all points/nodes of a tree, and the objective is to minimize the maximum of lengths of their tours. For location-allocation problems (where both optimal home locations of the salesman and their tours most be found), which are NP-complete, fast polynomial heuristics with worst-case relative error \((p-1)/(p+1)\) are presented.

68R10 Graph theory (including graph drawing) in computer science
Full Text: DOI Link
[1] I. Averbakh and O. Berman, A heuristic with worst-case analysis for minmax routing of two traveling salesmen on a tree, Discrete Appl. Math., forthcoming. · Zbl 0848.90117
[2] Franka, P.M.; Gendreau, M.; Laporte, G.; Muller, F., The m-travelling salesman problem with minmax objective, ()
[3] Frederickson, G.N.; Hecht, M.S.; Kim, C.E., Approximation algorithms for some routing problems, SIAM J. comput., 7, 178-193, (1978)
[4] Garey, M.; Johnson, D., Computers and intractability, (1979), Freeman San Francisco
[5] Laporte, G.; Desrochers, M.; Nobert, Y., Two exact algorithms for the distance-constrained vehicle routing problem, Networks, 14, 161-172, (1984) · Zbl 0538.90093
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.