Results 1 
4 of
4
Using Sparsification for Parametric Minimum Spanning Tree Problems
 Nordic J. Computing
, 1996
"... 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 t ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
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 nnode, medge 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...
Algorithmic techniques for geometric optimization
 In Computer Science Today: Recent Trends and Developments, Lecture Notes in Computer Science
, 1995
"... ..."
LinearTime Algorithms for Parametric Minimum Spanning Tree Problems on Planar Graphs
, 1995
"... A lineartime algorithm for the minimumratio spanning tree problem on planar graphs is presented. The algorithm is based on a new planar minimum spanning tree algorithm. The approach extends to other parametric minimum spanning tree problems on planar graphs and to other families of graphs having s ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
A lineartime algorithm for the minimumratio spanning tree problem on planar graphs is presented. The algorithm is based on a new planar minimum spanning tree algorithm. The approach extends to other parametric minimum spanning tree problems on planar graphs and to other families of graphs having small separators.
Optimal Parametric Search on Graphs of Bounded Treewidth
, 1994
"... We give lineartime algorithms for a class of parametric search problems on weighted graphs of bounded treewidth. We also discuss the implications of our results to approximate parametric search on planar graphs. ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
We give lineartime algorithms for a class of parametric search problems on weighted graphs of bounded treewidth. We also discuss the implications of our results to approximate parametric search on planar graphs.