Optimizing over the subtour polytope of the travelling salesman problem
Mathematical Programming: Series A and B
Biconnectivity approximations and graph carvings
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Survivable networks, linear programming relaxations and the parsimonious property
Mathematical Programming: Series A and B
A better approximation ratio for the minimum k-edge-connected spanning subgraph problem
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Hardness of Approximation for Vertex-Connectivity Network-Design Problems
APPROX '02 Proceedings of the 5th 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
Approximating minimum-size k-connected spanning subgraphs via matching
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Highly connected hypergraphs containing no two edge-disjoint spanning connected subhypergraphs
Discrete Applied Mathematics - Submodularity
On the Held-Karp relaxation for the asymmetric and symmetric traveling salesman problems
Mathematical Programming: Series A and B
Approximating the smallest k-edge connected spanning subgraph by LP-rounding
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Minimum Bounded Degree Spanning Trees
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Approximating minimum bounded degree spanning trees to within one of optimal
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Multicommodity demand flow in a tree and packing integer programs
ACM Transactions on Algorithms (TALG)
Iterated rounding algorithms for the smallest k-edge connected spanning subgraph
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
A 1.8 approximation algorithm for augmenting edge-connectivity of a graph from 1 to 2
ACM Transactions on Algorithms (TALG)
Unsplittable Flow in Paths and Trees and Column-Restricted Packing Integer Programs
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
An O(log n/ log log n)-approximation algorithm for the asymmetric traveling salesman problem
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
On k-column sparse packing programs
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
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In the k-edge-connected spanning subgraph problem we are given a graph (V, E) and costs for each edge, and want to find a minimum-cost F ⊂ E such that (V, F) is k-edge-connected. We show there is a constant ε 0 so that for all k 1, finding a (1 + ε)-approximation for k-ECSS is NP-hard, establishing a gap between the unit-cost and general-cost versions. Next, we consider the multi-subgraph cousin of k-ECSS, in which we purchase a multi-subset F of E, with unlimited parallel copies available at the same cost as the original edge. We conjecture that a (1+ Θ(1/k))-approximation algorithm exists, and we describe an approach based on graph decompositions applied to its natural linear programming (LP) relaxation. The LP is essentially equivalent to the Held-Karp LP for TSP and the undirected LP for Steiner tree. We give a family of extreme points for the LP which are more complex than those previously known.