Abstract
This paper contrasts two algorithms for finding a fundamental set of cycles for a connected graph. The first algorithm based on a PRUNING technique is known to have complexity 0(β(G)|V|2). The second algorithm based on a DEPTH FIRST SEARCH is shown to have complexity 0(β(G)|V|).
Keywords
- Span Tree
- Random Graph
- Incidence Matrix
- Depth First Search
- Pruning Technique
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
A. Aho, J. Hopcroft and J. Ullman. The Design and Analysis of Computer Algorithms. Addison Wesley, Reading, Mass. (1974).
M. Behzad and G. Chartrand. Introduction to the Theory of Graphs. Allyn and Bacon, Boston (1962).
C. Gotlieb and D. Cornell, Algorithms for finding a fundamental set of cycles for an undirected linear graph. Comm. ACM 10 (1967), 780–783.
J. Hopcroft and R. Tarjan. Efficient algorithms for graph manipulation (Algorithm 447). Comm. ACM 16 (1973), 372–378.
A. Nijenhuis and H. Wilf. Combinatorial Algorithms. Academic Press, New York (1975).
R. Read. Teaching Graph Theory to a Computer, Recent Progress in Combinatorics. Academic Press, New York (1969).
R. Tarjan. Depth first search and linear graph algorithms. Siam J. Comput. 1 (1972), 146–160.
G. Tarry. Le probleme des labyrinthes. Nouvelles Ann. de Math. 14 (1895), 187.
L. Weinberg. Network Analysis and Synthesis. McGraw-Hill, New York (1962).
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© 1978 Springer-Verlag Berlin Heidelberg
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Haggard, G. (1978). Pruning and depth first search. In: Alavi, Y., Lick, D.R. (eds) Theory and Applications of Graphs. Lecture Notes in Mathematics, vol 642. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0070379
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DOI: https://doi.org/10.1007/BFb0070379
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08666-6
Online ISBN: 978-3-540-35912-8
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