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

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.