Augmenting graphs to meet edge-connectivity requirements
SIAM Journal on Discrete Mathematics
The Steiner tree packing problem in VLSI design
Mathematical Programming: Series A and B
A primal-dual schema based approximation algorithm for the element connectivity problem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Approximating the Domatic Number
SIAM Journal on Computing
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Edge-disjoint trees containing some given vertices in a graph
Journal of Combinatorial Theory Series B
On decomposing a hypergraph into k connected sub-hypergraphs
Discrete Applied Mathematics - Submodularity
Hardness of Approximation for Vertex-Connectivity Network Design Problems
SIAM Journal on Computing
Iterative rounding 2-approximation algorithms for minimum-cost vertex connectivity problems
Journal of Computer and System Sciences - Special issue on FOCS 2001
Packing element-disjoint steiner trees
ACM Transactions on Algorithms (TALG)
Network design for vertex connectivity
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Approximate min--max theorems for Steiner rooted-orientations of graphs and hypergraphs
Journal of Combinatorial Theory Series B
Algorithms for Single-Source Vertex Connectivity
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
An almost O(log k)-approximation for k-connected subgraphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Approximate Integer Decompositions for Undirected Network Design Problems
SIAM Journal on Discrete Mathematics
Disjoint bases in a polymatroid
Random Structures & Algorithms
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
An improved approximation algorithm for minimum-cost subset k-connectivity
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
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Given an undirected graph G = (V ,E ) and subset of terminals T *** V , the element-connectivity *** *** G (u ,v ) of two terminals u ,v *** T is the maximum number of u -v paths that are pairwise disjoint in both edges and non-terminals V *** T (the paths need not be disjoint in terminals). Element-connectivity is more general than edge-connectivity and less general than vertex-connectivity. Hind and Oellermann [18] gave a graph reduction step that preserves the global element-connectivity of the graph. We show that this step also preserves local connectivity, that is, all the pairwise element-connectivities of the terminals. We give two applications of the step to connectivity and network design problems: First, we show a polylogarithmic approximation for the problem of packing element-disjoint Steiner forests in general graphs, and an O (1)-approximation in planar graphs. Second, we find a very short and intuitive proof of a spider-decomposition theorem of Chuzhoy and Khanna [10] in the context of the single-sink k -vertex-connectivity problem. Our results highlight the effectiveness of the element-connectivity reduction step; we believe it will find more applications in the future.