### Abstract

We consider a special subgraph of a weighted directed graph: one comprising only the k heaviest edges incoming to each vertex. We show that the maximum weight branching in this subgraph closely approximates the maximum weight branching in the original graph. Specifically, it is within a factor of k / ( k + 1 ). Our interest in finding branchings in this subgraph is motivated by a data compression application in which calculating edge weights is expensive but estimating which are the heaviest k incoming edges is easy. An additional benefit is that since algorithms for finding branchings run in time linear in the number of edges our results imply faster algorithms although we sacrifice optimality by a small factor. We also extend our results to the case of edge-disjoint branchings of maximum weight and to maximum weight spanning forests.

Original language | English (US) |
---|---|

Pages (from-to) | 54-58 |

Number of pages | 5 |

Journal | Information Processing Letters |

Volume | 99 |

Issue number | 2 |

DOIs | |

State | Published - Jul 31 2006 |

### Fingerprint

### Keywords

- Analysis of algorithms
- Graph algorithms

### ASJC Scopus subject areas

- Computational Theory and Mathematics

### Cite this

*Information Processing Letters*,

*99*(2), 54-58. https://doi.org/10.1016/j.ipl.2006.02.011

**Approximate maximum weight branchings.** / Bagchi, Amitabha; Bhargava, Ankur; Suel, Torsten.

Research output: Contribution to journal › Article

*Information Processing Letters*, vol. 99, no. 2, pp. 54-58. https://doi.org/10.1016/j.ipl.2006.02.011

}

TY - JOUR

T1 - Approximate maximum weight branchings

AU - Bagchi, Amitabha

AU - Bhargava, Ankur

AU - Suel, Torsten

PY - 2006/7/31

Y1 - 2006/7/31

N2 - We consider a special subgraph of a weighted directed graph: one comprising only the k heaviest edges incoming to each vertex. We show that the maximum weight branching in this subgraph closely approximates the maximum weight branching in the original graph. Specifically, it is within a factor of k / ( k + 1 ). Our interest in finding branchings in this subgraph is motivated by a data compression application in which calculating edge weights is expensive but estimating which are the heaviest k incoming edges is easy. An additional benefit is that since algorithms for finding branchings run in time linear in the number of edges our results imply faster algorithms although we sacrifice optimality by a small factor. We also extend our results to the case of edge-disjoint branchings of maximum weight and to maximum weight spanning forests.

AB - We consider a special subgraph of a weighted directed graph: one comprising only the k heaviest edges incoming to each vertex. We show that the maximum weight branching in this subgraph closely approximates the maximum weight branching in the original graph. Specifically, it is within a factor of k / ( k + 1 ). Our interest in finding branchings in this subgraph is motivated by a data compression application in which calculating edge weights is expensive but estimating which are the heaviest k incoming edges is easy. An additional benefit is that since algorithms for finding branchings run in time linear in the number of edges our results imply faster algorithms although we sacrifice optimality by a small factor. We also extend our results to the case of edge-disjoint branchings of maximum weight and to maximum weight spanning forests.

KW - Analysis of algorithms

KW - Graph algorithms

UR - http://www.scopus.com/inward/record.url?scp=33646357789&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646357789&partnerID=8YFLogxK

U2 - 10.1016/j.ipl.2006.02.011

DO - 10.1016/j.ipl.2006.02.011

M3 - Article

VL - 99

SP - 54

EP - 58

JO - Information Processing Letters

JF - Information Processing Letters

SN - 0020-0190

IS - 2

ER -