Polynomial counting in anonymous dynamic networks with applications to anonymous dynamic algebraic computations

Dariusz R. Kowalski, Miguel A. Mosteiro

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

Abstract

Starting with Michail, Chatzigiannakis, and Spirakis work [20], the problem of Counting the number of nodes in Anonymous Dynamic Networks has attracted a lot of attention. The problem is challenging because nodes are indistinguishable (they lack identifiers and execute the same program) and the topology may change arbitrarily from round to round of communication, as long as the network is connected in each round. The problem is central in distributed computing as the number of participants is frequently needed to make important decisions, such as termination, agreement, synchronization, and many others. A variety of algorithms built on top of mass-distribution techniques have been presented, analyzed, and also experimentally evaluated; some of them assumed additional knowledge of network characteristics, such as bounded degree or given upper bound on the network size. However, the question of whether Counting can be solved deterministically in sub-exponential time remained open. In this work, we answer this question positively by presenting Methodical Counting, which runs in polynomial time and requires no knowledge of network characteristics. Moreover, we also show how to extend Methodical Counting to compute the sum of input values and more complex functions without extra cost. Our analysis leverages previous work on random walks in evolving graphs, combined with carefully chosen alarms in the algorithm that control the process and its parameters. To the best of our knowledge, our Counting algorithm and its extensions to other algebraic and Boolean functions are the first that can be implemented in practice with worst-case guarantees.

Original languageEnglish (US)
Title of host publication45th International Colloquium on Automata, Languages, and Programming, ICALP 2018
EditorsChristos Kaklamanis, Daniel Marx, Ioannis Chatzigiannakis, Donald Sannella
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770767
DOIs
StatePublished - Jul 1 2018
Event45th International Colloquium on Automata, Languages, and Programming, ICALP 2018 - Prague, Czech Republic
Duration: Jul 9 2018Jul 13 2018

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume107
ISSN (Print)1868-8969

Other

Other45th International Colloquium on Automata, Languages, and Programming, ICALP 2018
CountryCzech Republic
CityPrague
Period7/9/187/13/18

Fingerprint

Polynomials
Boolean functions
Distributed computer systems
Synchronization
Topology
Communication
Costs

Keywords

  • Anonymous dynamic networks
  • Boolean functions
  • Counting
  • Deterministic algorithms
  • Distributed algorithms

ASJC Scopus subject areas

  • Software

Cite this

Kowalski, D. R., & Mosteiro, M. A. (2018). Polynomial counting in anonymous dynamic networks with applications to anonymous dynamic algebraic computations. In C. Kaklamanis, D. Marx, I. Chatzigiannakis, & D. Sannella (Eds.), 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018 [156] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 107). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ICALP.2018.156

Polynomial counting in anonymous dynamic networks with applications to anonymous dynamic algebraic computations. / Kowalski, Dariusz R.; Mosteiro, Miguel A.

45th International Colloquium on Automata, Languages, and Programming, ICALP 2018. ed. / Christos Kaklamanis; Daniel Marx; Ioannis Chatzigiannakis; Donald Sannella. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018. 156 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 107).

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

Kowalski, DR & Mosteiro, MA 2018, Polynomial counting in anonymous dynamic networks with applications to anonymous dynamic algebraic computations. in C Kaklamanis, D Marx, I Chatzigiannakis & D Sannella (eds), 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018., 156, Leibniz International Proceedings in Informatics, LIPIcs, vol. 107, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018, Prague, Czech Republic, 7/9/18. https://doi.org/10.4230/LIPIcs.ICALP.2018.156
Kowalski DR, Mosteiro MA. Polynomial counting in anonymous dynamic networks with applications to anonymous dynamic algebraic computations. In Kaklamanis C, Marx D, Chatzigiannakis I, Sannella D, editors, 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2018. 156. (Leibniz International Proceedings in Informatics, LIPIcs). https://doi.org/10.4230/LIPIcs.ICALP.2018.156
Kowalski, Dariusz R. ; Mosteiro, Miguel A. / Polynomial counting in anonymous dynamic networks with applications to anonymous dynamic algebraic computations. 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018. editor / Christos Kaklamanis ; Daniel Marx ; Ioannis Chatzigiannakis ; Donald Sannella. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018. (Leibniz International Proceedings in Informatics, LIPIcs).
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