Abstract. We consider the problem of designing a minimum cost access network to carry traffic from a set of endnodes to a core network. Trunks are available in Ktypes reflecting economies of scale . A trunk type with a high initial overhead cost has a low cost per unit bandwidth and a trunk type with a low overhead cost has a high cost per unit bandwidth.
We formulate the problem as an integer program. We first use a primal—dual approach to obtain a solution whose cost is within O(K 2 )of optimal. Typically the value of Kis small. This is the first combinatorial algorithm with an approximation ratio that is polynomial in Kand is independent of the network size and the total traffic to be carried. We also explore linear program rounding techniques and prove a better approximation ratio of O(K) . Both bounds are obtained under weak assumptions on the trunk costs.
Our primal—dual algorithm is motivated by the work of Jain and Vazirani on facility location . Our rounding algorithm is motivated by the facility location algorithm of Shmoys et al. .
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Matthew Andrews, Lisa Zhang Approximation Algorithms for Access Network Design . Algorithmica 34, 197–215 (2002). https://doi.org/10.1007/s00453-002-0968-3
- Key words. Access network design, Economies of scale, Primal—dual algorithm, LP-rounding, Approximation algorithms.