## Random Sampling and Greedy Sparsification for Matroid Optimization Problems. (1998)

Venue: | Mathematical Programming |

Citations: | 9 - 2 self |

### BibTeX

@ARTICLE{Karger98randomsampling,

author = {David R. Karger},

title = {Random Sampling and Greedy Sparsification for Matroid Optimization Problems.},

journal = {Mathematical Programming},

year = {1998},

volume = {82},

pages = {99--116}

}

### OpenURL

### Abstract

Random sampling is a powerful tool for gathering information about a group by considering only a small part of it. We discuss some broadly applicable paradigms for using random sampling in combinatorial optimization, and demonstrate the effectiveness of these paradigms for two optimization problems on matroids: finding an optimum matroid basis and packing disjoint matroid bases. Applications of these ideas to the graphic matroid led to fast algorithms for minimum spanning trees and minimum cuts. An optimum matroid basis is typically found by a greedy algorithm that grows an independent set into an the optimum basis one element at a time. This continuous change in the independent set can make it hard to perform the independence tests needed by the greedy algorithm. We simplify matters by using sampling to reduce the problem of finding an optimum matroid basis to the problem of verifying that a given fixed basis is optimum, showing that the two problems can be solved in roughly the same ...