Approximation algorithms for graph augmentation
Journal of Algorithms
Biconnectivity approximations and graph carvings
Journal of the ACM (JACM)
Performance Guarantees for Approximation Algorithms Depending on Parametrized Triangle Inequalities
SIAM Journal on Discrete Mathematics
On approximability of the minimum-cost k-connected spanning subgraph problem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Performance guarantees for the TSP with a parameterized triangle inequality
Information Processing Letters
Approximation algorithms for the TSP with sharpened triangle inequality
Information Processing Letters
Algorithmics for hard problems: introduction to combinatorial optimization, randomization, approximation, and heuristics
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Approximation Algorithms for Minimum Size 2-Connectivity Problems
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Approximations for ATSP with Parametrized Triangle Inequality
STACS '02 Proceedings of the 19th 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
CIAC '00 Proceedings of the 4th Italian Conference on Algorithms and Complexity
Polynomial Time Algorithms for Edge-Connectivity Augmentation of Hamiltonian Paths
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
On k-edge-connectivity problems with sharpened triangle inequality
CIAC'03 Proceedings of the 5th Italian conference on Algorithms and complexity
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
Augmenting the edge-connectivity of a spider tree
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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In this paper we investigate the problem of finding a 2- connected spanning subgraph of minimal cost in a complete and weighted graph G. This problem is known to be APX-hard, both for the edge- and for the vertex-connectivity case. Here we prove that the APX-hardness still holds even if one restricts the edge costs to an interval [1,1 + 驴], for an arbitrary small 驴 0. This result implies the first explicit lower bound on the approximability of the general problems.On the other hand, if the input graph satisfies the sharpened 脽-triangle inequality, then a (2/3 + 1/3, 脽/1-脽)-approximation algorithm is designed. This ratio tends to 1 with 脽 tending to 1/2, and it improves the previous known bound of 3/2, holding for graphs satisfying the triangle inequality, as soon as 脽 G by means of a set of edges of minimum cost is considered. This problem is known to admit a 2-approximation algorithm. Here we show that whenever the input graph satisfies the sharpened 脽-triangle inequality with 脽