Edge-connectivity augmentation problems
Journal of Computer and System Sciences
Parallel ear decomposition search (EDS) and st-numbering in graphs
Theoretical Computer Science
A matroid approach to finding edge connectivity and packing arborescences
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Fully dynamic algorithms for edge connectivity problems
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Algorithms for parallel k-vertex connectivity and sparse certificates
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
A linear time algorithm for triconnectivity augmentation (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Ambivalent data structures for dynamic 2-edge-connectivity and k smallest spanning trees
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Applications of a poset representation to edge connectivity and graph rigidity
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
On finding minimal 2-connected subgraphs
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Augmenting graphs to meet edge-connectivity requirements
SIAM Journal on Discrete Mathematics
Computing minimal spanning subgraphs in linear time
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Improved approximations for the Steiner tree problem
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for graph augmentation
Journal of Algorithms
Survivable networks, linear programming relaxations and the parsimonious property
Mathematical Programming: Series A and B
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On Finding a Smallest Augmentation to Biconnect a Graph
ISA '91 Proceedings of the 2nd International Symposium on Algorithms
Approximating biconnectivity in parallel
Proceedings of the seventh annual ACM symposium on Parallel algorithms and architectures
Improved approximation algorithms for uniform connectivity problems
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Improving biconnectivity approximation via local optimization
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Increasing the weight of minimum spanning trees
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
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
Directed network design with orientation constraints
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Approximating unweighted connectivity problems in parallel
Information and Computation
Approximation algorithms for minimum-cost k-vertex connected subgraphs
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Algorithmic aspects of topology control problems for ad hoc networks
Proceedings of the 3rd ACM international symposium on Mobile ad hoc networking & computing
Approximability of dense and sparse instances of minimum 2-connectivity, TSP and path problems
SODA '02 Proceedings of the thirteenth 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
Discrete Applied Mathematics - Special issue: Special issue devoted to the fifth annual international computing and combinatories conference (COCOON'99) Tokyo, Japan 26-28 July 1999
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 New Bound for the 2-Edge Connected Subgraph Problem
Proceedings of the 6th International IPCO Conference on Integer Programming and Combinatorial Optimization
Approximation Algorithms for a Directed Network Design Problem
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
A Hybrid GA for the Edge-Biconnectivity Augmentation Problem
PPSN VI Proceedings of the 6th International Conference on Parallel Problem Solving from Nature
Polynomial Time Algorithms for Edge-Connectivity Augmentation of Hamiltonian Paths
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
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
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
Survivable network design: the capacitated minimum spanning network problem
Information Processing Letters
Algorithmic aspects of topology control problems for ad hoc networks
Mobile Networks and Applications
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Papers - Volume 01
Vertex covering by paths on trees with its applications in machine translation
Information Processing Letters
Range assignment for biconnectivity and k-edge connectivity in wireless ad hoc networks
Mobile Networks and Applications
Max-Life Power Schedule for connectivity and biconnectivity in wireless ad hoc networks
Mobile Networks and Applications
Iterated rounding algorithms for the smallest k-edge connected spanning subgraph
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
An o(log2 k)-approximation algorithm for the k-vertex connected spanning subgraph problem
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
On k-connectivity problems with sharpened triangle inequality
Journal of Discrete Algorithms
Monotone Covering Problems with an Additional Covering Constraint
Mathematics of Operations Research
Vertex covering by paths on trees with its applications in machine translation
Information Processing Letters
On minimum power connectivity problems
Journal of Discrete Algorithms
On k-edge-connectivity problems with sharpened triangle inequality
CIAC'03 Proceedings of the 5th Italian conference on Algorithms and complexity
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
On minimum power connectivity problems
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Distributed approximation algorithms for finding 2-edge-connected subgraphs
OPODIS'07 Proceedings of the 11th international conference on Principles of distributed systems
Tree embeddings for two-edge-connected network design
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Relay placement for fault tolerance in wireless networks in higher dimensions
Computational Geometry: Theory and Applications
On the design of reliable wireless mesh network infrastructure with QoS constraints
Computer Networks: The International Journal of Computer and Telecommunications Networking
On the maximum size of a minimal k-edge connected augmentation
Journal of Combinatorial Theory Series B
Degree Bounded Network Design with Metric Costs
SIAM Journal on Computing
Approximating rational objectives is as easy as approximating linear ones
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Approximation schemes for minimum 2-connected spanning subgraphs in weighted planar graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Bicriteria network design via iterative rounding
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Power optimization for connectivity problems
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
On the L ∞ -norm of extreme points for crossing supermodular directed network LPs
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Approximation algorithms for the minimum cardinality two-connected spanning subgraph problem
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Tight approximation algorithm for connectivity augmentation problems
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
A 5/4-approximation algorithm for biconnecting a graph with a given hamiltonian path
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
Range augmentation problems in static ad-hoc wireless networks
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
Approximating minimum power covers of intersecting families and directed connectivity problems
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Designing hypergraph layouts to GMPLS routing strategies
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
GMPLS label space minimization through hypergraph layouts
Theoretical Computer Science
On finding two-connected subgraphs in planar graphs
Operations Research Letters
Finding 2-edge connected spanning subgraphs
Operations Research Letters
Iterated Rounding Algorithms for the Smallest k-Edge Connected Spanning Subgraph
SIAM Journal on Computing
Relay placement for two-connectivity
IFIP'12 Proceedings of the 11th international IFIP TC 6 conference on Networking - Volume Part II
Minimum weight 2-edge-connected spanning subgraphs in planar graphs
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
A 4/3-approximation algorithm for minimum 3-edge-connectivity
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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A spanning tree in a graph is the smallest connected spanning subgraph. Given a graph, how does one find the smallest (i.e., least number of edges) 2-connected spanning subgraph (connectivity refers to both edge and vertex connectivity, if not specified)? Unfortunately, the problem is known to be NP-hard.We consider the problem of finding a better approximation to the smallest 2-connected subgraph, by an efficient algorithm. For 2-edge connectivity, our algorithm guarantees a solution that is no more than 3/2 times the optimal. For 2-vertex connectivity, our algorithm guarantees a solution that is no more than 5/3 times the optimal. The previous best approximation factor is 2 for each of these problems. The new algorithms (and their analyses) depend upon a structure called a carving of a graph, which is of independent interest. We show that approximating the optimal solution to within an additive constant is NP-hard as well.We also consider the case where the graph has edge weights. For this case, we show that an approximation factor of 2 is possible in polynomial time for finding a k-edge connected spanning subgraph. This improves an approximation factor of 3 for k = 2, due to Frederickson and Ja´Ja´ [1981], and extends it for any k (with an increased running time though).