A heuristic with worst-case analysis for minimax routing of two travelling salesmen on a tree
Discrete Applied Mathematics
(p-1)/(p+1)-approximate algorithms for p-traveling salemen problems on a tree with minmax objective
Discrete Applied Mathematics
Discrete Applied Mathematics
A faster 2-approximation algorithm for the minmax p-traveling salesmen problem on a tree
Discrete Applied Mathematics
Approximating the Minmax Rooted-Subtree Cover Problem
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Location-Routing Problems with Distance Constraints
Transportation Science
Transportation Science
Combinatorial Optimization: Theory and Algorithms
Combinatorial Optimization: Theory and Algorithms
Approximations for minimum and min-max vehicle routing problems
Journal of Algorithms
Approximation hardness of min-max tree covers
Operations Research Letters
Operations Research Letters
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This paper studies a min-max location-routing problem, which aims to determine both the home depots and the tours for a set of vehicles to service all the customers in a given weighted graph, so that the maximum working time of the vehicles is minimized. The min-max objective is motivated by the needs of balancing or fairness in vehicle routing applications. We have proved that unless NP=P, it is impossible for the problem to have an approximation algorithm that achieves an approximation ratio of less than 4/3. Thus, we have developed the first constant ratio approximation algorithm for the problem. Moreover, we have developed new approximation algorithms for several variants, which improve the existing best approximation ratios in the previous literature.