# 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…

## One Citation

### Improved approximation for Fractionally Subadditive Network Design

- Computer Science, MathematicsInf. Process. Lett.
- 2020

## References

SHOWING 1-10 OF 26 REFERENCES

### Plane Gossip: Approximating rumor spread in planar graphs

- Computer ScienceLATIN
- 2018

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

- Mathematics, Computer ScienceProceedings 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

- Computer ScienceAlgorithmica
- 2010

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.

### A tight bound on approximating arbitrary metrics by tree metrics

- Computer Science, MathematicsSTOC '03
- 2003

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

- Mathematics, Computer ScienceSTOC
- 1978

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

- MathematicsSIGA
- 2007

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

- Computer Science, MathematicsOper. Res. Lett.
- 2013

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

- Computer ScienceMath. Oper. Res.
- 2011

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

- MathematicsFSTTCS
- 2003

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.