Two-Connected Spanning Subgraphs with at Most $\frac{10}{7}{OPT}$ Edges

@article{Heeger2017TwoConnectedSS,
  title={Two-Connected Spanning Subgraphs with at Most \$\frac\{10\}\{7\}\{OPT\}\$ Edges},
  author={Klaus Heeger and Jens Vygen},
  journal={SIAM J. Discret. Math.},
  year={2017},
  volume={31},
  pages={1820-1835}
}
We present a $\frac{10}{7}$-approximation algorithm for the minimum two-vertex-connected spanning subgraph problem. 
3 Citations
A 4/3-Approximation Algorithm for the Minimum 2-Edge Connected Subgraph Problem
TLDR
A factor 4/3 approximation algorithm for the problem of finding a minimum 2-edge connected spanning subgraph of a given undirected multigraph, based upon a reduction to a restricted class of graphs.
An Upper Bound of 7n/6 for the Minimum Size 2EC on Cubic 3-Edge Connected Graphs
TLDR
It is shown that every 3-edge connected cubic graph G=(V, E), with n=|V| allows a 2EC solution for G of size at most 7n/6, which improves upon Boyd, Iwata and Takazawa's guarantee of 6n/5.
Beating the Integrality Ratio for s-t-Tours in Graphs
  • Vera Traub, J. Vygen
  • Mathematics, Computer Science
    2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)
  • 2018
TLDR
This paper devise a polynomial-time algorithm for the s-t-path graph TSP with approximation ratio 1.497 and introduces several completely new techniques, including a new type of ear-decomposition, an enhanced ear induction that reveals a novel connection to matroid union, a stronger lower bound, and a reduction of general instances to instances in which s and t have small distance.

References

SHOWING 1-10 OF 19 REFERENCES
Improving on the 1.5-Approximation of a Smallest 2-Edge Connected Spanning Subgraph
We give a $\frac{17}{12}$-approximation algorithm for the following NP-hard problem: Given a simple undirected graph, find a 2-edge connected spanning subgraph that has the minimum number of edges.
Approximation Algorithms for the Minimum Cardinality Two-Connected Spanning Subgraph Problem
The minimum cardinality 2-connected spanning subgraph problem is considered. An approximation algorithm with a performance ratio of 9/7 ≈ 1.286 is presented. This improves the previous best ratio of
A 5/4-approximation algorithm for minimum 2-edge-connectivity
TLDR
A 5/4-approximation algorithm is presented for the minimum cardinality 2-edge-connected spanning subgraph problem in undirected graphs and is shown that the ratio is tight with respect to current lower bounds, and any further improvement is possible only if new lower bounds are discovered.
Improved approximation algorithms for biconnected subgraphs via better lower bounding techniques
TLDR
Better techniques to lower bound the size of the minimum subgraphs are provided, which allows us to achieve approximation factors of a and $ respectively, thereby improving on existing algorithms that achieve NP-hard results.
Improving biconnectivity approximation via local optimization
TLDR
This paper presents a new technique which can be used to further improve parallel approximation factors to 5/3 + {epsilon}, and reveals an algorithm with a factor of {alpha} + 1/5, where a is the approximation factor of any 2-edge connectivity approximation algorithm.
Approximating minimum-size k-connected spanning subgraphs via matching
  • J. Cheriyan, R. Thurimella
  • Mathematics, Computer Science
    Proceedings of 37th Conference on Foundations of Computer Science
  • 1996
TLDR
An efficient heuristic is presented for the problem of finding a minimum-size k-connected spanning subgraph of a given graph G=(V,E), which is simple, deterministic, and runs in time O(k|E|/sup 2/).
Shorter tours by nicer ears: 7/5-approximation for the graph-TSP, 3/2 for the path version, and 4/3 for two-edge-connected subgraphs
TLDR
The key new ingredient of all algorithms is a special kind of ear-decomposition optimized using forest representations of hypergraphs that provides the lower bounds that are used to deduce the approximation ratios.
On approximability of the minimum-cost k-connected spanning subgraph problem
TLDR
This work provides the first proof that Vfnhing a PTAS for the k-vertex-connectivitv nroblem in unweiehted graphs is NP-hard even for k = 2 aid for graphs of bocnded degree, and shows that the algorithmic results for Euclidean graphs cannot be extended to arbitrarily high dimensions.
Problems in graph connectivity
We consider optimization problems where the main constraint is connectivity. Finding minimum-cost subgraphs with connectivity requirements is a fundamental problem in network optimization. This
Biconnectivity approximations and graph carvings
TLDR
This work considers the problem of finding an approximation to the smallest 2-connected subgraph, by an efficient algorithm, and shows that an approximation factor of 2 is possible in polynomial time for finding a k-edge connected spanning subgraph.
...
1
2
...