Results 1 
4 of
4
A Randomized LinearTime Algorithm to Find Minimum Spanning Trees
, 1994
"... We present a randomized lineartime algorithm to find a minimum spanning tree in a connected graph with edge weights. The algorithm uses random sampling in combination with a recently discovered lineartime algorithm for verifying a minimum spanning tree. Our computational model is a unitcost ra ..."
Abstract

Cited by 115 (7 self)
 Add to MetaCart
We present a randomized lineartime algorithm to find a minimum spanning tree in a connected graph with edge weights. The algorithm uses random sampling in combination with a recently discovered lineartime algorithm for verifying a minimum spanning tree. Our computational model is a unitcost randomaccess machine with the restriction that the only operations allowed on edge weights are binary comparisons.
A linearwork parallel algorithm for finding . . .
, 1994
"... We give the first linearwork parallel algorithm for finding a minimum spanning tree. It is a randomized algorithm, and requires O(2log \Lambda n log n) expected time. It is a modification of the sequential lineartime algorithm of Klein and Tarjan. ..."
Abstract

Cited by 14 (1 self)
 Add to MetaCart
We give the first linearwork parallel algorithm for finding a minimum spanning tree. It is a randomized algorithm, and requires O(2log \Lambda n log n) expected time. It is a modification of the sequential lineartime algorithm of Klein and Tarjan.
Random Sampling and Greedy Sparsification for Matroid Optimization Problems.
 Mathematical Programming
, 1998
"... 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 ..."
Abstract

Cited by 9 (2 self)
 Add to MetaCart
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 ...