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Colorful path detection in vertex-colored temporal

Published online by Cambridge University Press:  18 August 2023

Riccardo Dondi  and
Mohammad Mehdi Hosseinzadeh Open the ORCID record for Mohammad Mehdi Hosseinzadeh [Opens in a new window]
Riccardo Dondi*
Affiliation:
University of Bergamo, Bergamo, Italy
Mohammad Mehdi Hosseinzadeh*
Affiliation:
University of Bergamo, Bergamo, Italy
*
Corresponding authors: Riccardo Dondi, Mohammad Mehdi Hosseinzadeh; Emails: riccardo.dondi@unibg.it, m.hosseinzadeh@unibg.it
Corresponding authors: Riccardo Dondi, Mohammad Mehdi Hosseinzadeh; Emails: riccardo.dondi@unibg.it, m.hosseinzadeh@unibg.it
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Abstract

Finding paths is a fundamental problem in graph theory and algorithm design due to its many applications. Recently, this problem has been considered on temporal graphs, where edges may change over a discrete time domain. The analysis of graphs has also taken into account the relevance of vertex properties, modeled by assigning to vertices labels or colors. In this work, we deal with a problem that, given a static or temporal graph, whose vertices are colored graph looks for a path such that (1) the vertices of the path have distinct colors and (2) that path includes the maximum number of colors. We analyze the approximation complexity of the problem on static and temporal graphs, and we prove an inapproximability bound. Then, we consider the problem on temporal graphs, and we design a heuristic for it. We present an experimental evaluation of our heuristic, both on synthetic and real-world graphs. The experimental results show that for many instances of the problem, our method is able to return near-optimal solutions.

Keywords

Temporal graphsgraph algorithmsgraph miningheuristicsapproximation complexity
Type
Research Article
Information
Network Science , Volume 11 , Issue 4 , December 2023 , pp. 615 - 631
Copyright
© The Author(s), 2023. Published by Cambridge University Press

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Footnotes

Action Editor: Prof. Ulrik Brandes

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