Online k-server routing problems

Authors:
Vincenzo Bonifaci;Leen Stougie
Affiliations:
,epartment of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, MB, The Netherlands;,epartment of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, MB, The Netherlands
Venue:
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Year:
2006

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Abstract

In an online k-server routing problem, a crew of k servers has to visit points in a metric space as they arrive in real time. Possible objective functions include minimizing the makespan (k-Traveling Salesman Problem) and minimizing the average completion time (k-Traveling Repairman Problem). We give competitive algorithms, resource augmentation results and lower bounds for k-server routing problems on several classes of metric spaces. Surprisingly, in some cases the competitive ratio is dramatically better than that of the corresponding single server problem. Namely, we give a 1+O((logk)/k)-competitive algorithm for the k-Traveling Salesman Problem and the k-Traveling Repairman Problem when the underlying metric space is the real line. We also prove that similar results cannot hold for the Euclidean plane.