## Greedy in Approximation Algorithms (2006)

Venue: | PROC. OF ESA |

Citations: | 13 - 1 self |

### BibTeX

@INPROCEEDINGS{Mestre06greedyin,

author = {Julián Mestre},

title = {Greedy in Approximation Algorithms},

booktitle = {PROC. OF ESA},

year = {2006},

publisher = {}

}

### OpenURL

### Abstract

The objective of this paper is to characterize classes of problems for which a greedy algorithm finds solutions provably close to optimum. To that end, we introduce the notion of k-extendible systems, a natural generalization of matroids, and show that a greedy algorithm is a 1-factor approximation for these systems. Many seemly unrelated k problems fit in our framework, e.g.: b-matching, maximum profit scheduling and maximum asymmetric TSP. In the second half of the paper we focus on the maximum weight b-matching problem. The problem forms a 2-extendible system, so greedy gives us a 1-factor solution which runs in 2 O(m log n) time. We improve this by providing two linear time approximation algorithms for the problem: a 1 2-factor algorithm that runs in O(bm) time, and a `2 3 − ǫ ´-factor algorithm which runs in expected O ` bm log 1 ´ time.