Two Algorithms for Computing All Spanning Trees of a Simple, Undirected, and Connected Graph: Once Assuming a Complete Graph

doi:10.1109/ACCESS.2018.2872737

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Two Algorithms for Computing All Spanning Trees of a Simple, Undirected, and Connected Graph: Once Assuming a Complete Graph

Journal Article•DOI•

Two Algorithms for Computing All Spanning Trees of a Simple, Undirected, and Connected Graph: Once Assuming a Complete Graph

Maumita Chakraborty¹, Sumon Chowdhury², Rajat Kumar Pal³•Institutions (3)

Information Technology Institute¹, Tata Consultancy Services², University of Calcutta³

01 Jan 2018-IEEE Access (Institute of Electrical and Electronics Engineers (IEEE))-Vol. 6, pp 56290-56300

TL;DR: This paper proposes altogether different and new approaches for the computation of all possible spanning trees of a simple, undirected, and connected graph and proposes to have novelties and limitations of its own.

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Abstract: In this paper, we have proposed altogether different and new approaches for the computation of all possible spanning trees of a simple, undirected, and connected graph. Our proposed algorithms have the capability to solve the major bottlenecks in this area, namely, generation of duplicate trees and circuit checking. In the first algorithm, the given graph has been converted to its corresponding weighted complete graph, which proposes to have novelties and limitations of its own. In addition, we have also proposed another related algorithm, and as a result, we have been able to come up with new ideas in this research domain of graph theory.

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Journal Article•DOI•

Divide-and-conquer based all spanning tree generation algorithm of a simple connected graph

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Dimitrios Gounopoulos¹•Institutions (1)

University of Engineering & Management¹

01 Jan 2022-Theoretical computer science

TL;DR: In this paper , an algorithm based on a new technique, namely divide-and-conquer, has been proposed for all spanning tree generation of a simple connected graph, which is a well-approached problem in graph theory.

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Abstract: All spanning tree generation of a simple connected graph is a well-approached problem in graph theory. In this paper, an algorithm based on a new technique, namely divide-and-conquer, has been proposed. The performance of the proposed algorithm has also been benchmarked against several existing algorithms, including one algorithm implemented in parallel, in this domain. The basis of comparison is on the number of circuits generated and CPU time taken by each of the algorithms compared, using a set of randomly generated graph instances on a common platform.

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3 citations

Book Chapter•DOI•

Algorithm to Generate All Spanning Tree Structures of a Complete Graph

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Suvrima Datta¹, Sumit Chakraborty², Maumita Chakraborty³, Rajat Kumar Pal¹•Institutions (3)

University of Calcutta¹, Ramsaday College², Information Technology Institute³

01 Jan 2021

TL;DR: In this article, the authors proposed an algorithm to generate all possible structures of spanning trees of an undirected complete graph of n vertices, where the process starts with a star-tree (T) of the given complete graph and then replaces the edges of T one by one to generate different possible structures like chain, branch, etc.

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Abstract: The objective of this paper is to propose an algorithm to generate all possible structures of spanning trees of an undirected complete graph of n vertices. The process starts with a star-tree (T) of the given complete graph and then replacing the edges of T one by one to generate different possible structures like chain, branch, etc. These spanning tree structures repeat themselves as we move from lower to higher values of n. The authors have attempted to find out some generalized expressions for different structures of spanning trees for a complete graph of order n.

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2 citations

References

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Journal Article•DOI•

Generation of All Spanning Trees of a Simple, Symmetric Connected Graph

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Krishnendu Basuli¹, Samar Sen Sarma¹, Saptarshi Naskar¹•Institutions (1)

University of Calcutta¹

30 Dec 2009-Social Science Research Network

TL;DR: This paper presents an algorithm for finding all possible spanning trees of a simple, connected and un-oriented graph by observing that generation of all spanning trees by test and select method is very much relevant today.

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Abstract: This paper presents an algorithm for finding all possible spanning trees of a simple, connected and un-oriented graph. To cope the situation we observed that generation of all spanning trees by test and select method is very much relevant today. As a sequel of our old work is the area we try here mainly all spanning tree generation with small amount of circuit checking. The time complexity of the algorithm is O(en n2 Tn) and space complexity of the algorithm is O(en), where n is the number of vertices and e is the number of edges of the graph. Although yet to reach the ideal situation that is the situation where we do not need any circuit checking for non-tree.

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4 citations

Journal Article•DOI•

New algorithm for generation of spanning trees

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B. V. Cherkasskii

01 Jan 1987-Cybernetics and Systems Analysis

4 citations

"Two Algorithms for Computing All Sp..." refers methods in this paper

...These three techniques are tree testing [1]–[10] elementary tree transformation [11]–[18], and successive reduction [19]–[21] methods....
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...[11] B. V. Cherkasskii, ‘‘New algorithm for generation of spanning trees,’’ Cybernetics, vol. 23, no. 1, pp. 107–113, 1987....
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...Some algorithms following this method of tree generation are those of Cherkasskii [11], Hakimi [12], Kapoor and Ramesh [13], Matsui [14], [15], Mayeda and Seshu [16], Shioura and Tamura [17], Shioura et al. [18], and many others. iii....
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...Some algorithms following this method of tree generation are those of Cherkasskii [11], Hakimi [12], Kapoor and Ramesh [13], Matsui [14], [15], Mayeda and Seshu [16], Shioura and Tamura [17], Shioura et al....
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Efficiently scanning all spanning trees of an undirected graph.

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Akiyoshi Shioura, Akihisa Tamura

01 Jun 1993

TL;DR: This paper proposes a new algorithm for enumerating all spanning trees of G in such compact form that is optimal in the sense of time complexity and space complexity.

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3 citations

"Two Algorithms for Computing All Sp..." refers methods in this paper

...[17] A. Shioura and A. Tamura, ‘‘Efficiently scanning all spanning trees of an undirected graph,’’ Dept. Inf....
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...[18] A. Shioura, A. Tamura, and T. Uno, ‘‘An optimal algorithm for scanning all spanning trees of undirected graphs,’’ SIAM J. Comput., vol. 26, no. 3, pp. 678–692, 1997....
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...Some algorithms following this method of tree generation are those of Cherkasskii [11], Hakimi [12], Kapoor and Ramesh [13], Matsui [14], [15], Mayeda and Seshu [16], Shioura and Tamura [17], Shioura et al....
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...Some algorithms following this method of tree generation are those of Cherkasskii [11], Hakimi [12], Kapoor and Ramesh [13], Matsui [14], [15], Mayeda and Seshu [16], Shioura and Tamura [17], Shioura et al. [18], and many others. iii....
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...Some of the earlier standard algorithms (namely, algorithms by Shioura and Tamura [17], Matsui [14], Mayeda and Seshu [16], Hakimi [12], Char [2], and Winter [21]) for generating all possible spanning trees of a given graph have also been implemented on the same environment with the same set of instances for a comparative study....
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