A strongly polynomial algorithm to solve combinatorial linear programs
Operations Research
Discrete Mathematics - Special volume (part two) to mark the centennial of Julius Petersen's “Die theorie der regula¨ren graphs” (“The theory of regular graphs”)
Approximating the tree and tour covers of a graph
Information Processing Letters
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
Provably good routing tree construction with multi-port terminals
Proceedings of the 1997 international symposium on Physical design
Rounding via trees: deterministic approximation algorithms for group Steiner trees and k-median
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A polylogarithmic approximation algorithm for the group Steiner tree problem
Journal of Algorithms
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
On approximability of the independent/connected edge dominating set problems
Information Processing Letters
On the terminal Steiner tree problem
Information Processing Letters
Integrality ratio for group Steiner trees and directed steiner trees
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Beyond Steiner's Problem: A VLSI Oriented Generalization
WG '89 Proceedings of the 15th International Workshop on Graph-Theoretic Concepts in Computer Science
Polylogarithmic inapproximability
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Approximation algorithms for set cover and related problems
Approximation algorithms for set cover and related problems
Theoretical Computer Science
Approximating connectivity augmentation problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A greedy approximation algorithm for the group Steiner problem
Discrete Applied Mathematics
How to trim an MST: a 2-approximation algorithm for minimum cost tree cover
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Set connectivity problems in undirected graphs and the directed Steiner network problem
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Graph Orientations with Set Connectivity Requirements
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Set connectivity problems in undirected graphs and the directed steiner network problem
ACM Transactions on Algorithms (TALG)
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Given a graph G= (V,E) with an edge cost and families $\mathcal{V}_i\subseteq 2^V$, i= 1,2,...,mof disjoint subsets, an edge subset F茂戮驴 Eis called a set connector if, for each $\mathcal{V}_i$, the graph $(V,F)/\mathcal{V}_i$ obtained from (V,F) by contracting each $X\in \mathcal{V}_i$ into a single vertex xhas a property that every two contracted vertices xand x茂戮驴 are connected in $(V,F)/\mathcal{V}_i$. In this paper, we introduce a problem of finding a minimum cost set connector, which contains several important network design problems such as the Steiner forest problem, the group Steiner tree problem, and the NA-connectivity augmentation problem as its special cases. We derive an approximate integer decomposition property from a fractional packing theorem of set connectors, and present a strongly polynomial 2茂戮驴-approximation algorithm for the set connector problem, where $\alpha=\max_{1 \leq i \leq m}(\sum_{X \in \mathcal{V}_i}|X|)-1$.