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Combinatorial Analysis of Growth Models for Series-Parallel Networks

Part of: Combinatorics Graph theory

Published online by Cambridge University Press:  14 August 2018

MARKUS KUBA  and
ALOIS PANHOLZER
MARKUS KUBA
Affiliation:
Institute of Applied Mathematics and Natural Sciences, University of Applied Sciences – Technikum Wien, Höchstädtplatz 5, 1200 Wien, Austria (e-mail: kuba@technikum-wien.at)
ALOIS PANHOLZER
Affiliation:
Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstraße 8-10/104, 1040 Wien, Austria (e-mail: Alois.Panholzer@tuwien.ac.at)
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Abstract

We give combinatorial descriptions of two stochastic growth models for series-parallel networks introduced by Hosam Mahmoud by encoding the growth process via recursive tree structures. Using decompositions of the tree structures and applying analytic combinatorics methods allows a study of quantities in the corresponding series-parallel networks. For both models we obtain limiting distribution results for the degree of the poles and the length of a random source-to-sink path, and furthermore we get asymptotic results for the expected number of source-to-sink paths. Moreover, we introduce generalizations of these stochastic models by encoding the growth process of the networks via further important increasing tree structures.

MSC classification

Primary: 05C80: Random graphs
Secondary: 05A15: Exact enumeration problems, generating functions 05A16: Asymptotic enumeration
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 28 , Special Issue 4: Analysis of Algorithms , July 2019 , pp. 574 - 599
Copyright
Copyright © Cambridge University Press 2018 

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Footnotes

†

The second author was supported by the Austrian Science Foundation FWF, grant P25337-N23.

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