Results 1 
4 of
4
An Empirical Analysis of Algorithms for Constructing a Minimum Spanning Tree
 DIMACS Series in Discrete Mathematics and Theoretical Computer Science
, 1991
"... We compare algorithms for the construction of a minimum spanning tree through largescale experimentation on randomly generated graphs of different structures and different densities. In order to extrapolate with confidence, we use graphs with up to 130,000 nodes (sparse) or 750,000 edges (dense). A ..."
Abstract

Cited by 21 (1 self)
 Add to MetaCart
(Show Context)
We compare algorithms for the construction of a minimum spanning tree through largescale experimentation on randomly generated graphs of different structures and different densities. In order to extrapolate with confidence, we use graphs with up to 130,000 nodes (sparse) or 750,000 edges (dense). Algorithms included in our experiments are Prim's algorithm (implemented with a variety of priority queues), Kruskal's algorithm (using presorting or demand sorting), Cheriton and Tarjan's algorithm, and Fredman and Tarjan 's algorithm. We also ran a large variety of tests to investigate lowlevel implementation decisions for the data structures, as well as to enable us to eliminate the effect of compilers and architectures. Within the range of sizes used, Prim's algorithm, using pairing heaps or sometimes binary heaps, is clearly preferable. While versions of Prim's algorithm using efficient implementations of Fibonacci heaps or rankrelaxed heaps often approach and (on the densest graphs) so...
Finding the k Smallest Spanning Trees
, 1992
"... We give improved solutions for the problem of generating the k smallest spanning trees in a graph and in the plane. Our algorithm for general graphs takes time O(m log #(m, n)+k 2 ); for planar graphs this bound can be improved to O(n + k 2 ). We also show that the k best spanning trees for a set of ..."
Abstract

Cited by 18 (2 self)
 Add to MetaCart
We give improved solutions for the problem of generating the k smallest spanning trees in a graph and in the plane. Our algorithm for general graphs takes time O(m log #(m, n)+k 2 ); for planar graphs this bound can be improved to O(n + k 2 ). We also show that the k best spanning trees for a set of points in the plane can be computed in time O(min(k 2 n + n log n, k 2 + kn log(n/k))). The k best orthogonal spanning trees in the plane can be found in time O(n log n + kn log log(n/k)+k 2 ).
How to Find a Minimum Spanning Tree in Practice
 results and New Trends in Computer Science, volume 555 of Lecture Notes in Computer Science
, 1991
"... We address the question of theoretical vs. practical behavior of algorithms for the minimum spanning tree problem. We review the factors that influence the actual running time of an algorithm, from choice of language, machine, and compiler, through lowlevel implementation choices, to purely algor ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
(Show Context)
We address the question of theoretical vs. practical behavior of algorithms for the minimum spanning tree problem. We review the factors that influence the actual running time of an algorithm, from choice of language, machine, and compiler, through lowlevel implementation choices, to purely algorithmic issues. We discuss how to design a careful experimental comparison between various alternatives. Finally, we present some results from an ongoing study in which we are using: multiple languages, compilers, and machines; all the major variants of the comparisonbased algorithms; and eight varieties of graphs with sizes of up to 130,000 vertices (in sparse graphs) or 750,000 edges (in dense graphs). 1 Introduction Finding spanning trees of minimum weight (minimum spanning trees or MSTs) is one of the best known graph problems; algorithms for this problem have a long history, for which see the article of Graham and Hell [6]. The best comparisonbased algorithm to date, due to Gabow...
Parallel Dynamic Algorithms for Minimum Spanning Trees
"... this paper, is the discovery that necessary information can be extracted without ever explicitly shrinking the components, as opposed to the approach undertaken in the third step of Chin, Lam and Chen's algorithm. Another difficulty is posed here by the exclusivewrite requirement, so that the ..."
Abstract
 Add to MetaCart
(Show Context)
this paper, is the discovery that necessary information can be extracted without ever explicitly shrinking the components, as opposed to the approach undertaken in the third step of Chin, Lam and Chen's algorithm. Another difficulty is posed here by the exclusivewrite requirement, so that the selection of the minimum cost edge to hook subtrees, seems to require either a powerful model of computation (as in Awerbuck and Shiloach's algorithm), or some minimization process (as in Chin, Lam and Chen's algorithm), which thereby takes time logarithmic in the length of the list. To overcome this difficulty, Johnson and Metaxas [23] modified the classical hook and contract scheme, providing a new approach to schedule the hooking of the subtrees in order to control their growth rate. Unlike the previous methods, in which every subforest could be doubled in size at each iteration of O(1) time, this algorithm can schedule every subforest to grow by a factor of at least 2 p log n in an iteration of O(log n) time. Hence, O( p log n) iterations suffices to find the final MST. Indeed, within a single 7 iteration of O(log n) time, slowgrowing components are scheduled to hook and contract in o(log n) time repeatedly until they catch up with fastgrowing components, and fastgrowing components are left idle once they achieve the intended size