Complexity of computation of a spanning tree enumeration algorithm

In 1968, Char [4] presented an algorithm to enumerate all the spanning trees of an undirected graph G . This algorithm starts with a known initial spanning tree of G , and generates all the other spanning trees along with certain spanning non-tree subgraphs of G . In this paper a detailed complexity...

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Bibliographic Details
Published inIEEE transactions on circuits and systems Vol. 31; no. 10; pp. 853 - 860
Main Authors Jayakumar, R., Thulasiraman, K., Swamy, M.
Format Journal Article
LanguageEnglish
Published IEEE 01.10.1984
Subjects
Algorithm design and analysis
Circuits
Computer science
Councils
Graph theory
Tree graphs
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ISSN0098-4094
DOI10.1109/TCS.1984.1085435

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Summary:In 1968, Char [4] presented an algorithm to enumerate all the spanning trees of an undirected graph G . This algorithm starts with a known initial spanning tree of G , and generates all the other spanning trees along with certain spanning non-tree subgraphs of G . In this paper a detailed complexity analysis of Char's algorithm and methods to speed up the algorithm are discussed. Two heuristics for the selection of the initial spanning tree are suggested. These heuristics result in a considerable reduction in the number of spanning non-tree subgraphs generated. A technique called path compression, aimed at reducing the actual number of comparisons, is described. Computational results on several randomly generated graphs are presented to illustrate the improvement achieved.
ISSN:0098-4094
DOI:10.1109/TCS.1984.1085435