Applications of submodular functions
Surveys in combinatorics, 1993
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
An Iterative Rounding 2-Approximation Algorithm for the Element Connectivity Problem
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
On the orientation of graphs and hypergraphs
Discrete Applied Mathematics - Submodularity
Combined connectivity augmentation and orientation problems
Discrete Applied Mathematics - Submodularity
An Approximate Max-Steiner-Tree-Packing Min-Steiner-Cut Theorem
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Algorithmic construction of sets for k-restrictions
ACM Transactions on Algorithms (TALG)
Network Coding for Efficient Wireless Unicast
IZS '06 Proceedings of the 2006 International Zurich Seminar on Communications
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Packing element-disjoint steiner trees
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
A Graph Reduction Step Preserving Element-Connectivity and Applications
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
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Given an undirected hypergraph and a subset of vertices S@?V with a specified root vertex r@?S, the Steiner Rooted-Orientation problem is to find an orientation of all the hyperedges so that in the resulting directed hypergraph the ''connectivity'' from the root r to the vertices in S is maximized. This is motivated by a multicasting problem in undirected networks as well as a generalization of some classical problems in graph theory. The main results of this paper are the following approximate min-max relations:*Given an undirected hypergraph H, if S is 2k-hyperedge-connected in H, then H has a Steiner rooted k-hyperarc-connected orientation. *Given an undirected graph G, if S is 2k-element-connected in G, then G has a Steiner rooted k-element-connected orientation. Both results are tight in terms of the connectivity bounds. These also give polynomial time constant factor approximation algorithms for both problems. The proofs are based on submodular techniques, and a graph decomposition technique used in the Steiner Tree Packing problem. Some complementary hardness results are presented at the end.