Reaching Consensus in Ad-Hoc Diffusion Networks

Dariusz R. Kowalski, Jarosław Mirek

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider an algorithmic model of diffusion networks, in which n nodes are distributed in a 2D Euclidean space and communicate by diffusing and sensing molecules. Such a model is interesting on its own right, although from the distributed computing point of view it may be seen as a generalization or even a framework for other wireless communication models, such as the SINR model, radio networks or the beeping model. Additionally, the diffusion networks model formalizes and generalizes recent case studies of simple processes in environment where nodes, often understood as biological cells, communicate by diffusing and sensing simple chemical molecules. To demonstrate the algorithmic nature of our model, we consider a fundamental problem of reaching consensus by nodes: in the beginning each node has some initial value, e.g., the reading from its sensor, and the goal is that each node outputs the same value. Our deterministic distributed algorithm runs at every node and outputs the consensus value equal to the sum of inputs divided by the sum of the channel coefficients of each cells. For a node v consensus is reached in (formula presented) communication rounds, where dv is the sum of molecule reachability ratios to node v in the medium, dmin=minidi, dmax=maxidi and b is the sum of the initial values. p represents the second largest eigenvalue of a matrix of normalised molecule reachability ratios, that we analyze together with an associated Markov Chain.

Original languageEnglish (US)
Title of host publicationAlgorithms for Sensor Systems - 14th International Symposium on Algorithms and Experiments for Wireless Sensor Networks, ALGOSENSORS 2018, Revised Selected Papers
EditorsSeth Gilbert, Danny Hughes, Bhaskar Krishnamachari
PublisherSpringer Verlag
Pages180-192
Number of pages13
ISBN (Print)9783030140939
DOIs
StatePublished - Jan 1 2019
Externally publishedYes
Event14th International Symposium on Algorithms and Experiments for Wireless Sensor Networks, ALGOSENSORS 2018 - Helsinki, Finland
Duration: Aug 23 2018Aug 24 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11410 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference14th International Symposium on Algorithms and Experiments for Wireless Sensor Networks, ALGOSENSORS 2018
CountryFinland
CityHelsinki
Period8/23/188/24/18

Fingerprint

Vertex of a graph
Molecules
Reachability
Sensing
Model
Communication
Distributed computer systems
Radio Networks
Output
Parallel algorithms
Cell
Largest Eigenvalue
Markov processes
Deterministic Algorithm
Diffusion Model
Distributed Algorithms
Distributed Computing
Wireless Communication
Network Model
Euclidean space

Keywords

  • Ad hoc networks
  • Cells
  • Consensus
  • Diffusion networks
  • Molecules

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Kowalski, D. R., & Mirek, J. (2019). Reaching Consensus in Ad-Hoc Diffusion Networks. In S. Gilbert, D. Hughes, & B. Krishnamachari (Eds.), Algorithms for Sensor Systems - 14th International Symposium on Algorithms and Experiments for Wireless Sensor Networks, ALGOSENSORS 2018, Revised Selected Papers (pp. 180-192). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11410 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-14094-6_12

Reaching Consensus in Ad-Hoc Diffusion Networks. / Kowalski, Dariusz R.; Mirek, Jarosław.

Algorithms for Sensor Systems - 14th International Symposium on Algorithms and Experiments for Wireless Sensor Networks, ALGOSENSORS 2018, Revised Selected Papers. ed. / Seth Gilbert; Danny Hughes; Bhaskar Krishnamachari. Springer Verlag, 2019. p. 180-192 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11410 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kowalski, DR & Mirek, J 2019, Reaching Consensus in Ad-Hoc Diffusion Networks. in S Gilbert, D Hughes & B Krishnamachari (eds), Algorithms for Sensor Systems - 14th International Symposium on Algorithms and Experiments for Wireless Sensor Networks, ALGOSENSORS 2018, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11410 LNCS, Springer Verlag, pp. 180-192, 14th International Symposium on Algorithms and Experiments for Wireless Sensor Networks, ALGOSENSORS 2018, Helsinki, Finland, 8/23/18. https://doi.org/10.1007/978-3-030-14094-6_12
Kowalski DR, Mirek J. Reaching Consensus in Ad-Hoc Diffusion Networks. In Gilbert S, Hughes D, Krishnamachari B, editors, Algorithms for Sensor Systems - 14th International Symposium on Algorithms and Experiments for Wireless Sensor Networks, ALGOSENSORS 2018, Revised Selected Papers. Springer Verlag. 2019. p. 180-192. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-030-14094-6_12
Kowalski, Dariusz R. ; Mirek, Jarosław. / Reaching Consensus in Ad-Hoc Diffusion Networks. Algorithms for Sensor Systems - 14th International Symposium on Algorithms and Experiments for Wireless Sensor Networks, ALGOSENSORS 2018, Revised Selected Papers. editor / Seth Gilbert ; Danny Hughes ; Bhaskar Krishnamachari. Springer Verlag, 2019. pp. 180-192 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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