Counting the Number of Paths in a Graph via BDDs

Kyoko SEKINE  Hiroshi IMAI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E80-A   No.4   pp.682-688
Publication Date: 1997/04/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
Category: 
Keyword: 
graphs,  paths,  #P-complete,  BDD,  

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Summary: 
This paper proposes a unified approach by means of the binary decision diagram, BDD in short, to solve #P-hand problems of counting the number of paths between two terminals in undirected and directed graphs. Our approach provides algorithms running in O (2O (n) ) time for typical planar graphs such as grid graphs. In fact, for any class of graphs having a good elimination ordering, this paradigm provides efficient solutions.