Construction of Simple Path Graphs in Transport Networks: II. Analysis of Graphs’ Biconnectivity

The problem of constructing all simple paths in an undirected graph that pairwise connect vertices from the given set is interpreted as constructing a graph that is a union of these paths. This construction relies on the computation of biconnected components and bridges of the source graph. A new al...

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Bibliographic Details
Published in:Journal of computer & systems sciences international 2021-03, Vol.60 (2), p.213-226
Main Author: Golovinskii, I. A.
Format: Article
Language:English
Subjects:
Algorithms
Apexes
Computation
Control
Engineering
Graph theory
Graphs
Mechatronics
Robotics
Systems Analysis and Operations Research
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Summary:The problem of constructing all simple paths in an undirected graph that pairwise connect vertices from the given set is interpreted as constructing a graph that is a union of these paths. This construction relies on the computation of biconnected components and bridges of the source graph. A new algorithm which makes this computation more transparent and controllable is proposed. Its idea is to track opening and closing of chords at the depth-first search. Due to the clarity of the proposed solution, its correctness is obvious without much justification. This is its advantage over the well-known Hopcroft–Tarjan algorithm. The proposed algorithm makes self-evident the obtaining biconnected components of a graph by successive uniting its fundamental cycles that have common edges.
ISSN:1064-2307
1555-6530
DOI:10.1134/S1064230721020040