A 3/2-approximation algorithm for some minimum-cost graph problems
- 464 Downloads
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 Classification90C27 05C85
We thank anonymous reviewers of this paper for useful comments.
- 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
- 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