A Graph Reduction Step Preserving Element-Connectivity and Applications
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Packing Steiner trees on four terminals
Journal of Combinatorial Theory Series B
Design is as Easy as Optimization
SIAM Journal on Discrete Mathematics
Packing of Steiner trees and S-connectors in graphs
Journal of Combinatorial Theory Series B
Degree Bounded Network Design with Metric Costs
SIAM Journal on Computing
Efficient edge splitting-off algorithms maintaining all-pairs edge-connectivities
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
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Given an undirected multigraph G and a subset of vertices S ⊆ 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 present 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 (S-trees) and the minimum size of an edge-cut that disconnects some pair of vertices in S (S-cut). Specifically, we prove that if every S-cut in G has at least 26k edges, then G has at least k edge-disjoint S-trees; this answers Kriesells conjecture affirmatively up to a constant multiple.