On the Greatest Number of Paths and Maximal Paths for a Class of Directed Acyclic Graphs

Shinsuke ODAGIRI; Hiroyuki GOTO

doi:10.1587/transfun.E97.A.1370

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

Online ISSN : 1745-1337
Print ISSN : 0916-8508

Special Section on Discrete Mathematics and Its Applications

On the Greatest Number of Paths and Maximal Paths for a Class of Directed Acyclic Graphs

Shinsuke ODAGIRI, Hiroyuki GOTO

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Keywords: directed acyclic graph, discrete event system, maximal path, PERT

JOURNAL RESTRICTED ACCESS

2014 Volume E97.A Issue 6 Pages 1370-1374

DOI https://doi.org/10.1587/transfun.E97.A.1370

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Abstract

For a fixed number of nodes, we focus on directed acyclic graphs in which there is not a shortcut. We find the case where the number of paths is maximized and its corresponding count of maximal paths. Considering this case is essential in solving large-scale scheduling problems using a PERT chart.

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