research-article

On a Class of Stochastic Multilayer Networks

Authors:

Saikat GuhaAuthors Info & Claims

Proceedings of the ACM on Measurement and Analysis of Computing Systems, Volume 2, Issue 1

Article No.: 18, Pages 1 - 25

https://doi.org/10.1145/3179421

Published: 03 April 2018 Publication History

Abstract

In this paper, we introduce a new class of stochastic multilayer networks. A stochastic multilayer network is the aggregation of M networks (one per layer) where each is a subgraph of a foundational network G. Each layer network is the result of probabilistically removing links and nodes from G. The resulting network includes any link that appears in at least K layers. This model is an instance of a non-standard site-bond percolation model. Two sets of results are obtained: first, we derive the probability distribution that the M-layer network is in a given configuration for some particular graph structures (explicit results are provided for a line and an algorithm is provided for a tree), where a configuration is the collective state of all links (each either active or inactive). Next, we show that for appropriate scalings of the node and link selection processes in a layer, links are asymptotically independent as the number of layers goes to infinity, and follow Poisson distributions. Numerical results are provided to highlight the impact of having several layers on some metrics of interest (including expected size of the cluster a node belongs to in the case of the line). This model finds applications in wireless communication networks with multichannel radios, multiple social networks with overlapping memberships, transportation networks, and, more generally, in any scenario where a common set of nodes can be linked via co-existing means of connectivity.

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Index Terms

On a Class of Stochastic Multilayer Networks
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Paths and connectivity problems
      2. Random graphs
2. Networks
  1. Network properties
    1. Network structure

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cover image Proceedings of the ACM on Measurement and Analysis of Computing Systems

Proceedings of the ACM on Measurement and Analysis of Computing Systems Volume 2, Issue 1

March 2018

603 pages

EISSN:2476-1249

DOI:10.1145/3203302

Editors:
Augustin Chaintreau
Columbia University
,
Aditya Akella
University of Wisconsin-Madison
,
Adam Wierman
California Institute of Technology

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Copyright © 2018 ACM.

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Publication History

Published: 03 April 2018

Published in POMACS Volume 2, Issue 1

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Cited By

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https://doi.org/10.1109/VCC60689.2023.10475021
Smolka SFoster NHsu JKappé TKozen DSilva A(2019)Guarded Kleene algebra with tests: verification of uninterpreted programs in nearly linear timeProceedings of the ACM on Programming Languages10.1145/33711294:POPL(1-28)Online publication date: 20-Dec-2019
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Chang SBallantyne MTurner MBowman W(2019)Dependent type systems as macrosProceedings of the ACM on Programming Languages10.1145/33710714:POPL(1-29)Online publication date: 20-Dec-2019
https://dl.acm.org/doi/10.1145/3371071
Clochard MMarché CPaskevich A(2019)Deductive verification with ghost monitorsProceedings of the ACM on Programming Languages10.1145/33710704:POPL(1-26)Online publication date: 20-Dec-2019
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Barbarossa DManzonetto G(2019)Taylor subsumes Scott, Berry, Kahn and PlotkinProceedings of the ACM on Programming Languages10.1145/33710694:POPL(1-23)Online publication date: 20-Dec-2019
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Jiang BNain PTowsley DGuha S(2019)On a Class of Stochastic Multilayer NetworksACM SIGMETRICS Performance Evaluation Review10.1145/3308809.330887146:1(119-121)Online publication date: 17-Jan-2019
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Altidor JHuang SSmaragdakis Y(2019)Taming the wildcardsACM SIGPLAN Notices10.1145/1993316.199356946:6(602-613)Online publication date: 28-Feb-2019
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Dillig IDillig TAiken ASagiv M(2019)Precise and compact modular procedure summaries for heap manipulating programsACM SIGPLAN Notices10.1145/1993316.199356546:6(567-577)Online publication date: 28-Feb-2019
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