Single-sink Fractionally Subadditive Network Design

@article{Guruganesh2017SinglesinkFS,
  title={Single-sink Fractionally Subadditive Network Design},
  author={Guru Guruganesh and Jennifer Iglesias and Ramamoorthi Ravi and Laura Sanit{\`a}},
  journal={ArXiv},
  year={2017},
  volume={abs/1707.01487}
}
We study a generalization of the Steiner tree problem, where we are given a weighted network $G$ together with a collection of $k$ subsets of its vertices and a root $r$. We wish to construct a minimum cost network such that the network supports one unit of flow to the root from every node in a subset simultaneously. The network constructed does not need to support flows from all the subsets simultaneously. We settle an open question regarding the complexity of this problem for $k=2$, and give… 
1 Citations

Figures from this paper

Improved approximation for Fractionally Subadditive Network Design

References

SHOWING 1-10 OF 26 REFERENCES

Plane Gossip: Approximating rumor spread in planar graphs

It is shown that the techniques for planar graphs extend to graphs with excluded minors, and polylogarithmic-approximation algorithms for both multi-commodity multicast and radio gossip problems in minor-free graphs are established.

A Factor 2 Approximation Algorithm for the Generalized Steiner Network Problem

  • K. Jain
  • Mathematics, Computer Science
    Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)
  • 1998
A factor 2 approximation algorithm for finding a minimum-cost subgraph having at least a specified number of edges in each cut, which first solves the linear relaxation of the generalized Steiner network problem, and then iteratively rounds off the solution.

Dynamic vs. Oblivious Routing in Network Design

The main result is a construction that shows that the optimal cost of such a network based on oblivious routing (fractional or integral) may be a factor of Ω(log n) more than the cost required when using dynamic routing.

An improved approximation algorithm for requirement cut

A tight bound on approximating arbitrary metrics by tree metrics

In this paper, we show that any n point metric space can be embedded into a distribution over dominating tree metrics such that the expected stretch of any edge is O(log n). This improves upon the

Node-and edge-deletion NP-complete problems

This paper shows that if &pgr; belongs to a rather broad class of properties then the node-deletion problem is NP-complete, and the same is true for several restrictions of it.

Routing and network design with robustness to changing or uncertain traffic demands

A survey of developments of the so-called hose model for demand matrices, which showed the existence of good randomized oblivious routings in all undirected graphs, and a proof of the polynomial time solvability of an optimal oblivious routing scheme are given.

Network design with a discrete set of traffic matrices

From Uncertainty to Nonlinearity: Solving Virtual Private Network via Single-Sink Buy-at-Bulk

The first constant factor approximation for concave VPN is given, and the best-known approximation factor for linear VPN is improved, and it is shown that VPN remains NP-hard even in the balanced case, where the sum of ingoing and outgoing traffic bounds is equal.

On the Covering Steiner Problem

The Covering Steiner problem is a common generalization of the k-MST and Group Steiner problems, where the problem is to find a minimum-cost tree which spans at least the required number of vertices from every group.