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arXiv · 1402.4183

An Improved Algorithm for Fixed-Hub Single Allocation Problem

Dongdong Ge·Zizhuo Wang·Lai Wei·Jiawei Zhang
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Abstract

This paper discusses the fixed-hub single allocation problem (FHSAP). In this problem, a network consists of hub nodes and terminal nodes. Hubs are fixed and fully connected; each terminal node is connected to a single hub which routes all its traffic. The goal is to minimize the cost of routing the traffic in the network. In this paper, we propose a linear programming (LP)-based rounding algorithm. The algorithm is based on two ideas. First, we modify the LP relaxation formulation introduced in Ernst and Krishnamoorthy (1996, 1999) by incorporating a set of validity constraints. Then, after obtaining a fractional solution to the LP relaxation, we make use of a geometric rounding algorithm to obtain an integral solution. We show that by incorporating the validity constraints, the strengthened LP often provides much tighter upper bounds than the previous methods with a little more computational effort, and the solution obtained often has a much smaller gap with the optimal solution. We also formulate a robust version of the FHSAP and show that it can guard against data uncertainty with little cost.

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Dongdong Ge, Zizhuo Wang, Lai Wei, Jiawei Zhang. 2014-02-17. An Improved Algorithm for Fixed-Hub Single Allocation Problem. https://arxiv.org/abs/1402.4183

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