Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
On finding lowest common ancestors: simplification and parallelization
SIAM Journal on Computing
Applications of a poset representation to edge connectivity and graph rigidity
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Biconnectivity approximations and graph carvings
Journal of the ACM (JACM)
Approximation algorithms for finding highly connected subgraphs
Approximation algorithms for NP-hard problems
A representation for crossing set families with applications to submodular flow problems
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Approximation Algorithms for Graph Augmentation
ICALP '92 Proceedings of the 19th International Colloquium on Automata, Languages and Programming
On 2-Coverings and 2-Packings of Laminar Families
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
Approximating minimum-size k-connected spanning subgraphs via matching
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
Vertex covering by paths on trees with its applications in machine translation
Information Processing Letters
A unified approach to approximating partial covering problems
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
A 1.8 approximation algorithm for augmenting edge-connectivity of a graph from 1 to 2
ACM Transactions on Algorithms (TALG)
Vertex covering by paths on trees with its applications in machine translation
Information Processing Letters
Covering a laminar family by leaf to leaf links
Discrete Applied Mathematics
A 1.5-approximation algorithm for augmenting edge-connectivity of a graph from 1 to 2
Information Processing Letters
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Augmenting the edge-connectivity of a spider tree
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Edge-Connectivity augmentation and network matrices
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Kernelization and complexity results for connectivity augmentation problems
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Fixed-Parameter algorithms for minimum cost edge-connectivity augmentation
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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Given a graph G=(V,E) and a tree T =(V,F) with E ∩ F = φ such that G + T =(V,F ∪ E) is 2-edge-connected, we consider the problem of finding a smallest 2-edge-connected spanning subgraph (V,F ∪ E') of G + T containing T. The problem, which is known to be NP-hard, admits a 2-approximation algorithm. However, obtaining a factor better than 2 for this problem has been one of the main open problems in the graph augmentation problem. In this paper, we show that the problem is (1.875 + ε)-approximable in O(n½m + n2) time for any constant ε n = |V| and m = |E ∪ F|.