Minimum-weight two-connected spanning networks
Mathematical Programming: Series A and B
Analyzing the Held-Karp TSP bound: a monotonicity property with application
Information Processing Letters
Survivable networks, linear programming relaxations and the parsimonious property
Mathematical Programming: Series A and B
Biconnectivity approximations and graph carvings
Journal of the ACM (JACM)
Worst-case comparison of valid inequalities for the TSP
Mathematical Programming: Series A and B
Improved approximation algorithms for network design problems
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Finding the Exact Integrality Gap for Small Traveling Salesman Problems
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Approximation Algorithms for Minimum Size 2-Connectivity Problems
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Factor 4/3 approximations for minimum 2-connected subgraphs
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
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Given a complete undirected graph with non-negative costs on the edges, the 2-Edge Connected Subgraph Problem consists in finding the minimum cost spanning 2-edge connected subgraph (where multiedges are allowed in the solution). A lower bound for the minimum cost 2-edge connected subgraph is obtained by solving the linear programming relaxation for this problem, which coincides with the subtour relaxation of the traveling salesman problem when the costs satisfy the triangle inequality. The simplest fractional solutions to the subtour relaxation are the 1/2 - integral solutions in which every edge variable has a value which is a multiple of 1/2. We show that the minimum cost of a 2-edge connected subgraph is at most four-thirds the cost of the minimum cost 1/2 -integral solution of the subtour relaxation. This supports the long-standing 4/3 Conjecture for the TSP, which states that there is a Hamilton cycle which is within 4/3 times the cost of the optimal subtour relaxation solution when the costs satisfy the triangle inequality.