SciELO - Scientific Electronic Library Online

 
 issue12Efeitos do Emprego público na produção privadaThe Interpretation of Verbal Probability Expressions Used in the IAS/IFRS: Some Portuguese Evidence author indexsubject indexarticles search
Home Pagealphabetic serial listing  

Services on Demand

Journal

Article

Indicators

Related links

  • Have no similar articlesSimilars in SciELO

Share


Tékhne - Revista de Estudos Politécnicos

Print version ISSN 1645-9911

Abstract

SIMOES, Ricardo. APAC: An exact algorithm for retrieving cycles and paths in all kinds of graphs. Tékhne [online]. 2009, n.12, pp.39-55. ISSN 1645-9911.

This paper presents an alorithm for retrieving all paths and all cycles between two vertices in random directed or undirected connected graphs. This algorithm can be easily implemented and is highly modular; with minor changes it can be adapted to obtain different parameters from the graphs. It is also demonstrated that the complexity of the algorithm increases linearly with the number of paths. The algorithm can be used in a myriad of applications. Aside from calculating all the paths and cycles in a graph, it can be used to calculate all the paths with length l between two vertices in the graph, as well as a solution to the clique decision problem. Thus, it has applications in computer networks, material science and electric networks, as well as in any problem where it is necessary to know the number of paths (not the optimal paths) in a directed or undirected connected graph or in multigraphs. The algorithms currently available in the literature, such as the depth-first search (DFS), are unable to solve this type of problems in a straightforward way.

Keywords : graph theory; connected graphs; random graphs; network paths; nanofiber networks.

        · abstract in Portuguese     · text in English     · English ( pdf )