On sparse spanners of weighted graphs
Discrete & Computational Geometry
Biconnectivity approximations and graph carvings
Journal of the ACM (JACM)
Approximation algorithms for finding highly connected subgraphs
Approximation algorithms for NP-hard problems
Efficient algorithms for constructing fault-tolerant geometric spanners
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Approximating geometrical graphs via “spanners” and “banyans”
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On approximability of the minimum-cost k-connected spanning subgraph problem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A polynomial-time approximation scheme for weighted planar graph TSP
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating minimum size {1,2}-connected networks
Discrete Applied Mathematics
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
A 5/4-approximation algorithm for minimum 2-edge-connectivity
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
A 2-Approximation for Minimum Cost {0, 1, 2} Vertex Connectivity
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
Fast Approximation Schemes for Euclidean Multi-connectivity Problems
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Polynomial-Time Approximation Schemes for the Euclidean Survivable Network Design Problem
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Factor 4/3 approximations for minimum 2-connected subgraphs
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
Approximation algorithm for k-node connected subgraphs via critical graphs
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
A linear-time approximation scheme for planar weighted TSP
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Approximation algorithms via contraction decomposition
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation Algorithms via Structural Results for Apex-Minor-Free Graphs
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Light spanners in bounded pathwidth graphs
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Minimum weight 2-edge-connected spanning subgraphs in planar graphs
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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We present new approximation schemes for various classical problems of finding the minimum-weight spanning subgraph in edge-weighted undirected planar graphs that are resistant to edge or vertex removal. We first give a PTAS for the problem of finding minimum-weight 2-edge-connected spanning subgraphs where duplicate edges are allowed. Then we present a new greedy spanner construction for edge-weighted planar graphs, which augments any connected subgraph A of a weighted planar graph G to a (1+ε)-spanner of G with total weight bounded by weight(A)/ε. From this we derive quasi-polynomial time approximation schemes for the problems of finding the minimum-weight 2-edge-connected or biconnected spanning subgraph in planar graphs. We also design approximation schemes for the minimum-weight 1-2-connectivity problem, which is the variant of the survivable network design problem where vertices have 1 or 2 connectivity constraints. Prior to our work, for all these problems no polynomial or quasi-polynomial time algorithms were known to achieve an approximation ratio better than 2.