Greedy algorithm and symmetric matroids
Mathematical Programming: Series A and B
Discrete Mathematics
Improved approximation algorithms for uniform connectivity problems
Journal of Algorithms
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
The primal-dual method for approximation algorithms and its application to network design problems
Approximation algorithms for NP-hard problems
Approximation algorithms for finding highly connected subgraphs
Approximation algorithms for NP-hard problems
Improved approximation algorithms for network design problems
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Approximation Algorithms for a Directed Network Design Problem
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
Approximating k-outconnected Subgraph Problems
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
A Factor 2 Approximation Algorithm for the Generalized Steiner Network Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Polynomial-Time Approximation Schemes for the Euclidean Survivable Network Design Problem
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Tree embeddings for two-edge-connected network design
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Constrained surface-level gateway placement for underwater acoustic wireless sensor networks
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
Approximation schemes for minimum 2-connected spanning subgraphs in weighted planar graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
On the L ∞ -norm of extreme points for crossing supermodular directed network LPs
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Constrained surface-level gateway placement for underwater acoustic wireless sensor networks
Theoretical Computer Science
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In survivable network design, each pair (i, j) of vertices is assigned a level of importance rij. The vertex connectivity problem is to design a minimum cost network such that between each pair of vertices with importance level r, there are r vertex disjoint paths. There is no approximation algorithm known for this general problem. In this paper, we give a 2-approximation for the problem when r ∈ {0, 1, 2}V × V, improving on a previous known 3-approximation. This matches the best known approximation for the easier problem that requires that the paths be only edge-disjoint. Our algorithm extends an iterative rounding algorithm that gives a 2-approximation for the edge-connectivity problem, for arbitrary connectivity requirements r. (K. Jain, A factor 2 approximation for the generalized Steiner network problem.) This algorithm relies on well-known uncrossing lemma for tight edge cutsets. Our extension uses a new type of uncrossing lemma for tight cutsets that may include vertices as well as edges. For r ∈ {1, k}V × V, k ≥ 3, we show that a) uncrossing tight cutsets is not possible, and b) any analysis for iterative rounding that depends directly on the largest fractional value in the linear programming solution cannot provide approximation guarantees better than the maximum connectivity requirement.