# Approximation algorithms for the capacitated minimum spanning tree problem and its variants in network design

@inproceedings{Jothi2005ApproximationAF, title={Approximation algorithms for the capacitated minimum spanning tree problem and its variants in network design}, author={R. Mary Jeya Jothi and Balaji Raghavachari}, booktitle={TALG}, year={2005} }

Given an undirected graph <i>G</i> = (<i>V,E</i>) withnonnegative costs on its edges, a root node <i>r</i> <i>V</i>, aset of demands <i>D</i> <i>V</i> with demand <i>v</i> <i>D</i>wishing to route <i>w(v)</i> units of flow (weight) to <i>r</i>,and a positive number <i>k</i>, the <i>Capacitated Minimum SteinerTree</i> (CMStT) problem asks for a minimum Steiner tree, rooted at<i>r</i>, spanning the vertices in <i>D</i> *{<i>r</i>}, in which the sum of the vertexweights in every subtree…

## 64 Citations

### On the approximation of the generalized capacitated tree-routing problem

- MathematicsJ. Discrete Algorithms
- 2010

### Approximating the Generalized Capacitated Tree-Routing Problem

- Computer ScienceCOCOON
- 2008

In this paper, we introduce the generalized capacitated tree-routing problem(GCTR), which is described as follows. Given a connected graph G= (V,E) with a sink si¾? Vand a set Mi¾? Vi¾? {s} of…

### An improved approximation algorithm for capacitated multicast routings in networks

- MathematicsTheor. Comput. Sci.
- 2008

### Approximation algorithms for single-sink edge installation problems and other graph problems

- Computer Science, Mathematics
- 2004

Many network design problems require designing networks that obey certain constraints. Minimum spanning tree, Steiner tree, vehicle routing, and facility location problems are examples. The goal is…

### Approximation Algorithms for Multicast Routings in a Network with Multi-Sources

- MathematicsIEICE Trans. Fundam. Electron. Commun. Comput. Sci.
- 2007

A (2ρUFL + ρST)-approximation algorithm to the CMMTR is proposed, where ρUFL and ρ ST are any approximation ratios achievable for the uncapacitated facility location and the Steiner tree problems, respectively.

### Approximating capacitated tree-routings in networks

- Computer ScienceJ. Comb. Optim.
- 2007

A (2+ρST)-approximation algorithm to CTR is proposed, where ρST is any approximation ratio achievable for the Steiner tree problem.

### Improved approximation algorithms for the single-sink buy-at-bulk network design problems

- MathematicsJ. Discrete Algorithms
- 2009

### Formulations for designing robust networks

- Mathematics, Computer Science
- 2017

This work searches for a minimum cost subset E′ ⊂ E, covering T and r, such that the network induced by E′ is k-survivable: after the removal of any k edges, there still exists a feasible flow from r to T .

### Survivable network design: the capacitated minimum spanning network problem

- Mathematics, Computer ScienceInf. Process. Lett.
- 2004

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