WAOA 2006: Approximation and Online Algorithms pp 188-201 | Cite as
Network Design with Edge-Connectivity and Degree Constraints
Conference paper
Abstract
We consider the following network design problem; Given a vertex set V with a metric cost c on V, an integer k≥1, and a degree specification b, find a minimum cost k-edge-connected multigraph on V under the constraint that the degree of each vertex v∈V is equal to b(v). This problem generalizes metric TSP. In this paper, we propose that the problem admits a ρ-approximation algorithm if b(v)≥2, v∈V, where ρ=2.5 if k is even, and ρ=2.5+1.5/k if k is odd. We also prove that the digraph version of this problem admits a 2.5-approximation algorithm and discuss some generalization of metric TSP.
Preview
Unable to display preview. Download preview PDF.
References
- 1.Frank, A.: Augmenting graphs to meet edge-connectivity requirements. SIAM Journal on Discrete Mathematics 5, 25–53 (1992)MATHCrossRefMathSciNetGoogle Scholar
- 2.Frank, A.: On a theorem of Mader. Discrete Mathematics 191, 49–57 (1992)CrossRefGoogle Scholar
- 3.Frederickson, G.N., Hecht, M.S., Kim, C.E.: Approximation algorithms for some routing problems. SIAM Journal of Computing 7, 178–193 (1978)CrossRefMathSciNetGoogle Scholar
- 4.Fukunaga, T., Nagamochi, H.: Approximating minimum cost multigraphs of specified edge-connectivity under degree bounds. In: Proceedings of the 9th Japan-Korea Joint Workshop on Algorithm and Computation, pp. 25–32 (2006)Google Scholar
- 5.Fukunaga, T., Nagamochi, H.: Approximating a generalization of metric TSP. IEICE Transactions on Information and Systems (to appear)Google Scholar
- 6.Goemans, M.X., Bertsimas, D.J.: Survivable networks, linear programming relaxations and the parsimonious property. Mathematical Programming 60, 145–166 (1993)MATHCrossRefMathSciNetGoogle Scholar
- 7.Goemans, M.X., Williamson, D.P.: The primal-dual method for approximation algorithms and its application to network design problems, Ch. 4, pp. 144–191. PWS (1997)Google Scholar
- 8.Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., Shmoys, D.B.: The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization. John Wiley & Sons, Chichester (1985)MATHGoogle Scholar
- 9.Mader, W.: A reduction method for edge-connectivity in graphs. Annals of Discrete Mathematics 3, 145–164 (1978)MATHCrossRefMathSciNetGoogle Scholar
- 10.Schrijver, A.: Combinatorial Optimization: Polyhedra and Efficiency. Springer, Heidelberg (2003)MATHGoogle Scholar
- 11.Vazirani, V.: Approximation Algorithm. Springer, Heidelberg (2001)Google Scholar
- 12.Wolsey, L.A.: Heuristic analysis, linear programming and branch and bound. Mathematical Programming Study 13, 121–134 (1980)MATHMathSciNetGoogle Scholar
Copyright information
© Springer-Verlag Berlin Heidelberg 2007