Title 



An algorithm for generating spanning trees of a graph in order of increasing cost
 
Author 



 
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 kth 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.   
Language 



English
 
Source (journal) 



Pesquisa Operacional  
Publication 



2005
 
ISSN 



01017438
 
Volume/pages 



25:2(2005), p. 219229
 
Full text (open access) 


  
