TY - JOUR
T1 - Unranking and ranking spanning trees of a graph
AU - Colbourn, Charles J.
AU - Day, Robert P.J.
AU - Nel, Louis D.
N1 - Funding Information:
Thanks to Wendy Myrvold and Bill Pulleyblank for helpful discussions about this research. The research of the first author is supported by NSERC Canada under Grant AO579.
PY - 1989/6
Y1 - 1989/6
N2 - The set S of spanning trees of an n-vertex graph G can be placed in one-to-one correspondence with the integers in the interval [1, s], where s = |S|. We develop O(n3) unranking and ranking functions for the spanning trees of an arbitrary graph. The unranking function maps any interval [1, s] to the corresponding tree, while the ranking function maps a spanning tree to the appropriate index in the interval. The unranking function provides an O(n3) method for generating a random spanning tree of a graph with uniform distribution.
AB - The set S of spanning trees of an n-vertex graph G can be placed in one-to-one correspondence with the integers in the interval [1, s], where s = |S|. We develop O(n3) unranking and ranking functions for the spanning trees of an arbitrary graph. The unranking function maps any interval [1, s] to the corresponding tree, while the ranking function maps a spanning tree to the appropriate index in the interval. The unranking function provides an O(n3) method for generating a random spanning tree of a graph with uniform distribution.
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U2 - 10.1016/0196-6774(89)90016-3
DO - 10.1016/0196-6774(89)90016-3
M3 - Article
AN - SCOPUS:38249021927
SN - 0196-6774
VL - 10
SP - 271
EP - 286
JO - Journal of Algorithms
JF - Journal of Algorithms
IS - 2
ER -