An algorithm to generate all spanning trees of a graph in order of increasing cost
Document title: An algorithm to generate all spanning trees of a graph in order of increasing cost
Journal: Pesquisa operacional
Database: PERIÓDICA
System number: 000313110
ISSN: 0101-7438
Authors: 1
2
Institutions: 1University of Antwerp, Amberes. Bélgica
2Hasselt University, Diepenbeek. Bélgica
Year:
Season: May-Ago
Volumen: 25
Number: 2
Pages: 219-229
Country: Brasil
Language: Inglés
Document type: Artículo
Approach: Experimental
English abstract A minimum spanning tree of an undirected graph can be easily obtained using classical algorithms by Prim or Kruskal. A number of algorithms have been proposed to enumerate all spanning trees of an undirected graph. Good time and space complexities are the major concerns of these algorithms. Most algorithms generate spanning trees using some fundamental cut or circuit. In the generation process, the cost of the tree is not taken into consideration. This paper presents an algorithm to generate spanning trees of a graph in order of increasing cost. By generating spanning trees in order of increasing cost, new opportunities appear. In this way, it is possible to determine the second smallest or, in general, the k-th smallest spanning tree. The smallest spanning tree satisfying some additional constraints can be found by checking at each generation whether these constraints are satisfied. Our algorithm is based on an algorithm by Murty (1967), which enumerates all solutions of an assignment problem in order of increasing cost. Both time and space complexities are discussed
Disciplines: Matemáticas,
Ciencias de la computación
Keyword: Matemáticas aplicadas,
Programación,
Complejidad computacional,
Weighted spanning trees,
Enumeración,
Algoritmos
Keyword: Mathematics,
Computer science,
Applied mathematics,
Programming,
Computational complexity,
Weighted spanning trees,
Enumeration,
Algorithms
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