## Using Sparsification for Parametric Minimum Spanning Tree Problems (1996)

Venue: | Nordic J. Computing |

Citations: | 7 - 2 self |

### BibTeX

@ARTICLE{Fernández-baca96usingsparsification,

author = {David Fernández-baca and Giora Slutzki and David Eppstein},

title = {Using Sparsification for Parametric Minimum Spanning Tree Problems},

journal = {Nordic J. Computing},

year = {1996},

volume = {3},

pages = {352--366}

}

### OpenURL

### Abstract

Two applications of sparsification to parametric computing are given. The first is a fast algorithm for enumerating all distinct minimum spanning trees in a graph whose edge weights vary linearly with a parameter. The second is an asymptotically optimal algorithm for the minimum ratio spanning tree problem, as well as other search problems, on dense graphs. 1 Introduction In the parametric minimum spanning tree problem, one is given an n-node, m-edge undirected graph G where each edge e has a linear weight function w e (#)=a e +#b e . Let Z(#) denote the weight of the minimum spanning tree relative to the weights w e (#). It can be shown that Z(#) is a piecewise linear concave function of # [Gus80]; the points at which the slope of Z changes are called breakpoints. We shall present two results regarding parametric minimum spanning trees. First, we show that Z(#) can be constructed in O(min{nm log n, TMST (2n, n) # Department of Computer Science, Iowa State University, Ames, IA...