A 3/2-approximation algorithm for some minimum-cost graph problems
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Abstract
We consider a class of graph problems introduced in a paper of Goemans and Williamson that involve finding forests of minimum edge cost. This class includes a number of location/routing problems; it also includes a problem in which we are given as input a parameter \(k\), and want to find a forest such that each component has at least \(k\) vertices. Goemans and Williamson gave a 2-approximation algorithm for this class of problems. We give an improved 3/2-approximation algorithm.
Mathematics Subject Classification
90C27 05C85Notes
Acknowledgments
We thank anonymous reviewers of this paper for useful comments.
References
- 1.Couëtoux, B.: A 3/2 approximation for a constrained forest problem. In: Demetrescu, C., Halldórsson, M.M. (eds.) Algorithms—ESA 2011, 19th Annual European Symposium, no. 6942 in Lecture Notes in Computer Science, pp. 652–663. Springer (2011)Google Scholar
- 2.Davis, J.M., Williamson, D.P.: A dual-fitting 3/2-approximation algorithm for some minimum-cost graph problems. In: Epstein, L., Ferragina, P. (eds.) Algorithms—ESA 2012, 20th Annual European Symposium, no. 7501 in Lecture Notes in Computer Science, pp. 373–382. Springer (2012)Google Scholar
- 3.Imielińska, C., Kalantari, B., Khachiyan, L.: A greedy heuristic for a minimum-weight forest problem. Oper. Res. Lett. 14, 65–71 (1993)CrossRefzbMATHMathSciNetGoogle Scholar
- 4.Bazgan, C., Couëtoux, B., Tuza, Z.: Complexity and approximation of the constrained forest problem. Theor. Comput. Sci. 412, 4081–4091 (2011)CrossRefzbMATHGoogle Scholar
- 5.Kruskal, J.: On the shortest spanning subtree of a graph and the traveling salesman problem. Proc. Am. Math. Soc. 7, 48–50 (1956)CrossRefzbMATHMathSciNetGoogle Scholar
- 6.Laszlo, M., Mukherjee, S.: Another greedy heuristic for the constrained forest problem. Oper. Res. Lett. 33, 629–633 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
- 7.Laszlo, M., Mukherjee, S.: A class of heuristics for the constrained forest problem. Discret. Appl. Math. 154, 6–14 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
- 8.Goemans, M.X., Williamson, D.P.: Approximating minimum-cost graph problems with spanning tree edges. Oper. Res. Lett. 16, 183–189 (1994)CrossRefzbMATHMathSciNetGoogle Scholar
- 9.Laszlo, M., Mukherjee, S.: An approximation algorithm for network design problems with downwards-monotone demand functions. Optim. Lett. 2, 171–175 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
- 10.Goemans, M.X., Williamson, D.P.: The primal-dual method for approximation algorithms and its application to network design problems. In: Hochbaum, D.S. (ed.) Approximation Algorithms for NP-Hard Problems, Chap. 4. PWS Publishing, Boston, MA (1996)Google Scholar
- 11.Byrka, J., Grandoni, F., Rothvoß, T., Sanità, L.: Steiner tree approximation via iterative randomized rounding. J. ACM 60, Art no. 6 (2013)Google Scholar
- 12.Archer, A., Bateni, M., Hajiaghayi, M., Karloff, H.: Improved approximation algorithms for prize-collecting Steiner tree and TSP. SIAM J. Comput. 40, 309–332 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
- 13.Goemans, M.X., Williamson, D.P.: A general approximation technique for constrained forest problems. SIAM J. Comput. 24, 296–317 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
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