On the capacity of information networks
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Packing element-disjoint steiner trees
ACM Transactions on Algorithms (TALG)
On routing in VLSI design and communication networks
Discrete Applied Mathematics
Approximate min--max theorems for Steiner rooted-orientations of graphs and hypergraphs
Journal of Combinatorial Theory Series B
Using Multicast Transfers in the Replica Migration Problem: Formulation and Scheduling Heuristics
Euro-Par '09 Proceedings of the 15th International Euro-Par Conference on Parallel Processing
A constant bound on throughput improvement of multicast network coding in undirected networks
IEEE Transactions on Information Theory
Packing trees in communication networks
WINE'05 Proceedings of the First international conference on Internet and Network Economics
Disjoint cycles: integrality gap, hardness, and approximation
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
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
Design is as easy as optimization
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
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Given an undirected multigraph G and a subset of vertices S 驴 V (G), the STEINER TREE PACKING problem is to find a largest collection of edge-disjoint trees that each connects S. This problem and its generalizations have attracted considerable attention from researchers in different areas because of their wide applicability. This problem was shown to be APX-hard (no polynomial time approximation scheme unless P=NP). In fact, prior to this paper, not even an approximation algorithm with asymptotic ratio o(n) was known despite several attempts. In this work, we close this huge gap by presenting the first polynomial time constant factor approximation algorithm for the STEINER TREE PACKING problem. The main theorem is an approximate min-max relation between the maximum number of edge-disjoint trees that each connects S (i.e. S-trees) and the minimum size of an edge-cut that disconnects some pair of vertices in S (i.e. S-cut). Specifically, we prove that if the minimum S-cut in G has 26k edges, then G has at least k edge-disjoint S-trees; this answers Kriesell's conjecture affirmatively up to a constant multiple. The techniques that we use are purely combinatorial, where matroid theory is the underlying ground work.