article

Free access

Algorithm 422: minimal spanning tree [H]

Author:

V. Kevin M. WhitneyAuthors Info & Claims

Communications of the ACM, Volume 15, Issue 4

Pages 273 - 274

https://doi.org/10.1145/361284.361299

Published: 01 April 1972 Publication History

PDF eReader

Abstract

This algorithm generates a spanning tree of minimal total edge length for an undirected graph specified by an array of inter-node edge lengths using a technique suggested by Dijkstra [1]. Execution time is proportional to the square of the number of nodes of the graph; a minimal spanning tree for a graph of 50 nodes is generated in 0.1 seconds on an IBM System 360/67. Previous algorithms [2, 3, 4, 5] require an amount of computation which depends on the graph topology and edge lengths and are best suited to graphs with few edges.

Supplementary Material

GZ File (422.gz)

minimal spanning tree

Download
12.00 KB

References

[1]

Dijkstra, E.W. A note on two problems in connection with graphs. Numer. Math. 1, 5 (Oct. 1959), 269-271.

Digital Library

Google Scholar

[2]

Kruskal, J.B. Jr. On the shortest spanning subtree of a graph and the traveling salesman problem. Proc. Amer. Math. Soc. 7 (1956), 48-50.

Crossref

Google Scholar

[3]

Prim, R.C. Shortest connection networks and some generalizations. Bell Syst. Tech. J. 36 (Nov. 1957), 1389-1401.

Crossref

Google Scholar

[4]

Obruca, A. Algorithm 1. MINTREE, Comput. Bull. (Sept. 1964), 67.

Google Scholar

[5]

Loberman, H., and Weinberger, A. Formal procedures for connecting terminals with a minimum total wire length. J. ACM 4, 4 (Oct. 1957), 428-437.

Digital Library

Google Scholar

[6]

Lawler, E.L. An Introduction to Combinatorial Optimization Theory and Its Applications, 2 vols. Holt, Rinehart & Winston, New York, 1971.

Google Scholar

[7]

Forsythe, G.E., and Moler, C.B. Computer Solution of Linear Algebraic Systems. Prentice-Hall, Englewood Cliffs, N.J., 1967.

Google Scholar

[8]

Moler, Cleve B. Matrix computations with Fortran and paging. Comm. ACM 15 (Apr. 1972), 268-270.

Digital Library

Google Scholar

Cited By

View all

Sztein MBafford ASalerno-Goncalves R(2020)Salmonella enterica serovar Typhi exposure elicits ex vivo cell-type-specific epigenetic changes in human gut cellsScientific Reports10.1038/s41598-020-70492-210:1Online publication date: 12-Aug-2020
https://doi.org/10.1038/s41598-020-70492-2
Steele JShepp LEddy W(2016)On the number of leaves of a euclidean minimal spanning treeJournal of Applied Probability10.2307/321420724:04(809-826)Online publication date: 14-Jul-2016
https://doi.org/10.2307/3214207
Steele JShepp LEddy W(2016)On the number of leaves of a euclidean minimal spanning treeJournal of Applied Probability10.1017/S002190020011670524:04(809-826)Online publication date: 14-Jul-2016
https://doi.org/10.1017/S0021900200116705
Show More Cited By

Recommendations

An exact algorithm for the Maximum Leaf Spanning Tree problem

Given an undirected graph with n vertices, the Maximum Leaf Spanning Tree problem is to find a spanning tree with as many leaves as possible. When parameterized in the number of leaves k, this problem can be solved in time O(4kpoly(n)) using a simple ...
Spanning trees and spanning Eulerian subgraphs with small degrees

Liu and Xu (1998) and Ellingham, Nam and Voss (2002) independently showed that every k -edge-connected simple graph G has a spanning tree T such that for each vertex v , d T ( v ) d ( v ) k + 2 . In this paper we show that every k -edge-connected graph ...
Spanning Trees with Many Leaves in Graphs With Minimum Degree Three

We present two lower bounds for the maximum number of leaves over all spanning trees of a graph. For connected, triangle-free graphs on $n$ vertices, with minimum degree at least three, we show that a spanning tree with at least $(n+4)/3$ leaves exists. ...

Comments

Information & Contributors

Information

Published In

Communications of the ACM Volume 15, Issue 4

April 1972

70 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/361284

Editor:
M. Stuart Lynn
Rice Univ., Houston, TX

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 April 1972

Published in CACM Volume 15, Issue 4

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

45
Total Citations
View Citations
885
Total Downloads

Downloads (Last 12 months)65
Downloads (Last 6 weeks)3

Reflects downloads up to 15 Oct 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Sztein MBafford ASalerno-Goncalves R(2020)Salmonella enterica serovar Typhi exposure elicits ex vivo cell-type-specific epigenetic changes in human gut cellsScientific Reports10.1038/s41598-020-70492-210:1Online publication date: 12-Aug-2020
https://doi.org/10.1038/s41598-020-70492-2
Steele JShepp LEddy W(2016)On the number of leaves of a euclidean minimal spanning treeJournal of Applied Probability10.2307/321420724:04(809-826)Online publication date: 14-Jul-2016
https://doi.org/10.2307/3214207
Steele JShepp LEddy W(2016)On the number of leaves of a euclidean minimal spanning treeJournal of Applied Probability10.1017/S002190020011670524:04(809-826)Online publication date: 14-Jul-2016
https://doi.org/10.1017/S0021900200116705
Van Gassen SCallebaut BVan Helden MLambrecht BDemeester PDhaene TSaeys Y(2015)FlowSOM: Using self‐organizing maps for visualization and interpretation of cytometry dataCytometry Part A10.1002/cyto.a.2262587:7(636-645)Online publication date: 8-Jan-2015
https://doi.org/10.1002/cyto.a.22625
Lee D(2007)Low cost drainage networksNetworks10.1002/net.32300604056:4(351-371)Online publication date: 2-Mar-2007
https://doi.org/10.1002/net.3230060405
Roman HAlbergante MColombo MCroccolo FMarini FRiccardi C(2006)Modeling cross correlations within a many-assets marketPhysical Review E10.1103/PhysRevE.73.03612973:3Online publication date: 28-Mar-2006
https://doi.org/10.1103/PhysRevE.73.036129
Gavish B(2006)Topological design of centralized computer networks—formulations and algorithmsNetworks10.1002/net.323012040212:4(355-377)Online publication date: 11-Oct-2006
https://doi.org/10.1002/net.3230120402
Jiang XBunke H(2005)Optimal vertex ordering of a graph and its application to symmetry detectionGraph-Theoretic Concepts in Computer Science10.1007/3-540-55121-2_14(148-158)Online publication date: 5-Jun-2005
https://doi.org/10.1007/3-540-55121-2_14
Kasyanov VEvstigneev VKasyanov VEvstigneev V(2000)Spanning TreesGraph Theory for Programmers10.1007/978-94-011-4122-2_3(121-173)Online publication date: 2000
https://doi.org/10.1007/978-94-011-4122-2_3
Chaomei Chen Davies J(1999)Integrating spatial, semantic, and social structures for knowledge managementProceedings of the 32nd Annual Hawaii International Conference on Systems Sciences. 1999. HICSS-32. Abstracts and CD-ROM of Full Papers10.1109/HICSS.1999.772792(10)Online publication date: 1999
https://doi.org/10.1109/HICSS.1999.772792
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Abstract

Supplementary Material

References

Cited By

Recommendations

An exact algorithm for the Maximum Leaf Spanning Tree problem

Spanning trees and spanning Eulerian subgraphs with small degrees

Spanning Trees with Many Leaves in Graphs With Minimum Degree Three

Comments

Information

Published In

Publisher

Publication History

Permissions

Check for updates

Author Tags

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

PDF

eReader

Get Access

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations