A 5/4-approximation algorithm for minimum 2-edge-connectivity

A 5/4-approximation algorithm is presented for the minimum cardinality 2-edge-connected spanning subgraph problem in undirected graphs. This improves the previous best approximation ratio of 4/3. It is shown that our ratio is tight with respect to current lower bounds, and any further improvement is possible only if new lower bounds are discovered.

[1]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[2]  J. Edmonds.  Matroid Intersection , 2022 .

[3]  David Hartvigsen,et al.  The Square-Free 2-Factor Problem in Bipartite Graphs , 1999, IPCO.

[4]  Zoltán Szigeti,et al.  Improving on the 1.5-Approximation of a Smallest 2-Edge Connected Spanning Subgraph , 2001, SIAM J. Discret. Math..

[5]  Samir Khuller,et al.  Improved approximation algorithms for uniform connectivity problems , 1995, STOC '95.

[6]  Cristina G. Fernandes.  A better approximation ratio for the minimum k-edge-connected spanning subgraph problem , 1997, SODA '97.

[7]  Harold N. Gabow,et al.  An ear decomposition approach to approximating the smallest 3-edge connected spanning subgraph of a multigraph , 2002, SODA '02.

[8]  Santosh S. Vempala,et al.  Factor 4/3 approximations for minimum 2-connected subgraphs , 2000, APPROX.

[9]  Toshihide Ibaraki,et al.  A linear-time algorithm for finding a sparsek-connected spanning subgraph of ak-connected graph , 1992, Algorithmica.

[11]  David S. Johnson,et al.  Computers and In stractability: A Guide to the Theory of NP-Completeness. W. H Freeman, San Fran , 1979 .

[12]  Santosh S. Vempala,et al.  Approximation algorithms for minimum-cost k-vertex connected subgraphs , 2002, STOC '02.

[13]  Piotr Krysta,et al.  Approximation Algorithms for Minimum Size 2-Connectivity Problems , 2001, STACS.

[14]  Santosh S. Vempala,et al.  Improved approximation algorithms for biconnected subgraphs via better lower bounding techniques , 1993, SODA '93.

[15]  Andrzej Lingas,et al.  On approximability of the minimum-cost k-connected spanning subgraph problem , 1999, SODA '99.

[16]  Joseph Cheriyan,et al.  Approximating minimum-size k-connected spanning subgraphs via matching , 1996, Proceedings of 37th Conference on Foundations of Computer Science.

[17]  Harold N. Gabow.  Better performance bounds for finding the smallest k-edge connected spanning subgraph of a multigraph , 2003, SODA '03.

[18]  A. Frank,et al.  An application of submodular flows , 1989 .

[19]  Samir Khuller,et al.  Biconnectivity approximations and graph carvings , 1992, STOC '92.

[20]  Jayme Luiz Szwarcfiter,et al.  Hamilton Paths in Grid Graphs , 1982, SIAM J. Comput..