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doi:10.22028/D291-31049
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: | https://link.springer.com/chapter/10.1007/978-3-319-99154-2_10 |
Link to this record: | hdl:20.500.11880/29199 http://dx.doi.org/10.22028/D291-31049 |
ISBN: | 978-3-319-99153-5 978-3-319-99154-2 |
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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