Abstract

This article presents two simple deterministic algorithms for finding the Minimum Spanning Tree in O(|V| + |E|) time for any proper class of graphs closed on graph minors, which includes planar graphs and graphs of bounded genus. Both algorithms require no a priori knowledge of the structure of the class except for its density; edge weights are only compared and no random access to data is needed.

Citations

141	Trans-dichotomous algorithms for minimum spanning trees and shortest paths - Fredman, Willard - 1990
139	Data structures for on-line updating of minimum spanning trees - Frederickson - 1983
66	On the history of the minimum spanning tree problem - Hell, Graham - 1985
59	A minimum spanning tree algorithm with inverse-ackermann type complexity - Chazelle
38	Data Structures and Network Algorithms, volume 44 - Tarjan - 1983
37	An optimal minimum spanning tree algorithm - Pettie, Ramachandran
7	Otakar Bor˚uvka on Minimum Spanning Tree Problem - Neˇsetˇril, Milková, et al.
6	The minimum spanning tree problem on a planar graph - Matsui - 1995
5	jistém problému minimálním (About a Certain Minimal Problem), Práce mor. pˇrírodověd. spol. v Brně - Bor˚uvka, O - 1926
3	Some remarks on the history of MST-problem - Neˇsetˇril - 1997
3	Finding minimum spanning trees in O(mα(m, n)) time - Pettie - 1999
3	Finding minimum spanning trees in O(m(m;n)) time - Pettie - 1999
2	Colorings and Homomorphism of Minor Closed Classes - Nesetril, Mendez - 2002
1	Linear expected-time algorithms for connectivity problems - Karger, Klein, et al. - 1995
1	Data structures and network algorithms, 44 - Tarjan - 1983
1	O jistem problemu minimalnm (About a Certain Minimal Problem). Prace mor. prrodoved. spol. v Brne - Boruvka - 1926
1	Some remarks on the history of MST-problem - Nesetril - 1997