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arXiv · 1612.02990

Approximation Algorithm for Cycle-Star Hub Network Design Problems and Cycle-Metric Labeling Problems

Yuko Kuroki·Tomomi Matsui
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Abstract

We consider a single allocation hub-and-spoke network design problem which allocates each non-hub node to exactly one of given hub nodes so as to minimize the total transportation cost. This paper deals with a case in which the hubs are located in a cycle, which is called a cycle-star hub network design problem. The problem is essentially equivalent to a cycle-metric labeling problem. The problem 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 by a convex combination of Monge matrices.

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Yuko Kuroki, Tomomi Matsui. 2016-12-09. Approximation Algorithm for Cycle-Star Hub Network Design Problems and Cycle-Metric Labeling Problems. https://arxiv.org/abs/1612.02990

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