Approximation algorithms for NP-hard problems
Approximation algorithms for finding highly connected subgraphs
Approximation algorithms for NP-hard problems
Combinatorial optimization
A Factor 2 Approximation Algorithm for the Generalized Steiner Network Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
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
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
Multicommodity demand flow in a tree and packing integer programs
ACM Transactions on Algorithms (TALG)
A 1.8 approximation algorithm for augmenting edge-connectivity of a graph from 1 to 2
ACM Transactions on Algorithms (TALG)
Max-Weight Integral Multicommodity Flow in Spiders and High-Capacity Trees
Approximation and Online Algorithms
Multicommodity demand flow in a tree
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Covering a laminar family by leaf to leaf links
Discrete Applied Mathematics
Tree embeddings for two-edge-connected network design
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Cover-decomposition and polychromatic numbers
ESA'11 Proceedings of the 19th European conference on Algorithms
On the integrality ratio for tree augmentation
Operations Research Letters
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Let H be a laminar family of subsets of a groundset V . A k-cover of H is a multiset C of edges on V such that for every subset S in H, C has at least k edges that have exactly one end in S. A k-packing of H is a multiset P of edges on V such that for every subset S in H, P has at most k 驴 u(S) edges that have exactly one end in S. Here, u assigns an integer capacity to each subset in H.Our main results are: (a) Given a k-cover C of H, there is an efficient algorithm to find a 1-cover contained in C of size 驴 k|C|/(2k - 1). For 2-covers, the factor of 2/3 is best possible. (b) Given a 2-packing P of H, there is an efficient algorithm to find a 1-packing contained in P of size 驴 |P|/3. The factor of 1/3 for 2-packings is best possible.These results are based on efficient algorithms for finding appropriate colorings of the edges in a k-cover or a 2-packing, respectively, and they extend to the case where the edges have nonnegative weights. Our results imply approximation algorithms for some NP-hard problems in connectivity augmentation and related topics. In particular, we have a 4/3-approximation algorithm for the following problem: Given a tree T and a set of nontree edges E that forms a cycle on the leaves of T, find a minimum-size subset E' of E such that T + E' is 2-edge connected.