When trees collide: an approximation algorithm for the generalized Steiner problem on networks
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Biconnectivity approximations and graph carvings
Journal of the ACM (JACM)
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Improved approximation algorithms for network design problems
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for directed Steiner problems
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
A Factor 2 Approximation Algorithm for the Generalized Steiner Network Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
A 2-Approximation for Minimum Cost {0, 1, 2} Vertex Connectivity
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
Edge Covers of Setpairs and the Iterative Rounding Method
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
An approximation algorithm for MAX DICUT with given sizes of parts
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
| Hi-index | 0.01 |
We present a 2-approximation algorithm for a class of directed network design problems. The network design problem is to find a minimum cost subgraph such that for each vertex set S there are at least f(S) arcs leaving the set S. In the last 10 years general techniques have been developed for designing approximation algorithms for undirected network design problems. Recently, Kamal Jain gave a 2-approximation algorithm for the case when the function f is weakly supermodular. There has been very little progress made on directed network design problems. The main techniques used for the undirected problems do not extend to the directed case. András Frank has shown that in a special case when the function f is intersecting supermodular the problem can be solved optimally. In this paper, we use this result to get a 2-approximation algorithm for a more general case when f is crossing supermodular. We also extend Jain's techniques to directed problems. We prove that if the function f is crossing supermodular, then any basic solution of the LP relaxation of our problem contains at least one variable with value greater or equal to 1/4.