Journal of Graph Algorithms and Applications
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Special Issue on Selected Papers from the 11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017
Approximation Algorithm for Cycle-Star Hub Network Design Problems and Cycle-Metric Labeling Problems
Yuko Kuroki and Tomomi Matsui
Vol. 23, no. 1, pp. 93-110, 2019. Regular paper.
Abstract We consider a single allocation hub-and-spoke network design problem which allocates each non-hub node to exactly one of the given hub nodes in order to minimize the total transportation cost. This paper deals with a cycle-star hub network design problem, in which the hubs are located in a cycle. This problem is essentially equivalent to a cycle-metric labeling problem. It is useful in the design of networks in telecommunications and airline transportation systems. We propose a $2(1-1/h)$-approximation algorithm, where $h$ denotes the number of hub nodes. Our algorithm solves a linear relaxation problem and employs a dependent rounding procedure. We analyze our algorithm by approximating a given cycle-metric matrix using a convex combination of Monge matrices.
Submitted: August 2017.
Reviewed: May 2018.
Revised: June 2018.
Reviewed: July 2018.
Revised: August 2018.
Accepted: August 2018.
Final: August 2018.
Published: January 2019.