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Advances in Probability and Mathematical StatisticsAsymptotic Connectedness of Random Interval Graphs in a One Dimensional Data Delivery Problem

Advances in Probability and Mathematical Statistics: Asymptotic Connectedness of Random Interval... [In this work we present a probabilistic analysis of random interval graphs associated with randomly generated instances of the Data Delivery on a Line Problem (DDLP) (Chalopin et al., Data delivery by energy-constrained mobile agents on a line. In Automata, languages, and programming, pp. 423–434. Springer, Berlin, 2014). Random Interval Graphs have been previously studied by Scheinermann (Discrete Math 82:287–302, 1990). However, his model and ours provide different ways to generate the graphs. Our model is defined by how the agents in the DDLP may move, thus its importance goes beyond the intrinsic interest of random graphs and has to do with the complexity of a combinatorial optimization problem which has been proven to be NP-complete (Chalopin et al., Data delivery by energy-constrained mobile agents on a line. In Automata, languages, and programming, pp. 423–434. Springer, Berlin, 2014). We study the relationship between solvability of a random instance of the DDLP with respect to its associated interval graph connectedness. This relationship is important because through probabilistic analysis we prove that despite the NP-completeness of DDLP, there are classes of instances that can be solved polynomially.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Advances in Probability and Mathematical StatisticsAsymptotic Connectedness of Random Interval Graphs in a One Dimensional Data Delivery Problem

Part of the Progress in Probability Book Series (volume 79)
Editors: Hernández‐Hernández, Daniel; Leonardi, Florencia; Mena, Ramsés H.; Pardo Millán, Juan Carlos
Andrade Sernas, Caleb Erubiel; Calvillo Vives, Gilberto; Manrique Mirón, Paulo Cesar; Treviño Aguilar, Erick
Advances in Probability and Mathematical Statistics — Aug 5, 2021
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References (8)

Publisher
Springer International Publishing
Copyright
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
ISBN
978-3-030-85324-2
Pages
1 –21
DOI
10.1007/978-3-030-85325-9_1
Publisher site
See Chapter on Publisher Site

Abstract

[In this work we present a probabilistic analysis of random interval graphs associated with randomly generated instances of the Data Delivery on a Line Problem (DDLP) (Chalopin et al., Data delivery by energy-constrained mobile agents on a line. In Automata, languages, and programming, pp. 423–434. Springer, Berlin, 2014). Random Interval Graphs have been previously studied by Scheinermann (Discrete Math 82:287–302, 1990). However, his model and ours provide different ways to generate the graphs. Our model is defined by how the agents in the DDLP may move, thus its importance goes beyond the intrinsic interest of random graphs and has to do with the complexity of a combinatorial optimization problem which has been proven to be NP-complete (Chalopin et al., Data delivery by energy-constrained mobile agents on a line. In Automata, languages, and programming, pp. 423–434. Springer, Berlin, 2014). We study the relationship between solvability of a random instance of the DDLP with respect to its associated interval graph connectedness. This relationship is important because through probabilistic analysis we prove that despite the NP-completeness of DDLP, there are classes of instances that can be solved polynomially.]

Published: Aug 5, 2021

Keywords: Connectedness analysis; Data delivery problem; Mobile agents; Random interval graph

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