Please use this identifier to cite or link to this item: doi:10.22028/D291-31049
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Title: Lumping the Approximate Master Equation for Multistate Processes on Complex Networks
Author(s): Großmann, Gerrit
Kyriakopoulos, Charalampos
Bortolussi, Luca
Wolf, Verena
Editor(s): McIver, Annabelle
Horvath, Andras
Language: English
Title: Quantitative evaluation of systems : 15th International Conference
Startpage: 157
Endpage: 172
Publisher/Platform: Springer
Year of Publication: 2018
Place of publication: Cham
Title of the Conference: QEST 2018
Place of the conference: Beijing, China
Publikation type: Conference Paper
Abstract: Complex networks play an important role in human society and in nature. Stochastic multistate processes provide a powerful framework to model a variety of emerging phenomena such as the dynamics of an epidemic or the spreading of information on complex networks. In recent years, mean-field type approximations gained widespread attention as a tool to analyze and understand complex network dynamics. They reduce the model’s complexity by assuming that all nodes with a similar local structure behave identically. Among these methods the approximate master equation (AME) provides the most accurate description of complex networks’ dynamics by considering the whole neighborhood of a node. The size of a typical network though renders the numerical solution of multistate AME infeasible. Here, we propose an efficient approach for the numerical solution of the AME that exploits similarities between the differential equations of structurally similar groups of nodes. We cluster a large number of similar equations together and solve only a single lumped equation per cluster. Our method allows the application of the AME to real-world networks, while preserving its accuracy in computing estimates of global network properties, such as the fraction of nodes in a state at a given time.
DOI of the first publication: 10.1007/978-3-319-99154-2_10
URL of the first publication:
Link to this record: hdl:20.500.11880/29199
ISBN: 978-3-319-99153-5
Date of registration: 28-May-2020
Notes: Lecture notes in computer science ; volume 11024
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Informatik
Professorship: MI - Prof. Dr. Verena Wolf
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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