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Documents authored by Friedetzky, Tom

Document
DOI: 10.4230/LIPIcs.DISC.2018.10
A Population Protocol for Exact Majority with O(log5/3 n) Stabilization Time and Theta(log n) States

Authors: Petra Berenbrink, Robert Elsässer, Tom Friedetzky, Dominik Kaaser, Peter Kling, and Tomasz Radzik

Published in: LIPIcs, Volume 121, 32nd International Symposium on Distributed Computing (DISC 2018)

Abstract
A population protocol is a sequence of pairwise interactions of n agents. During one interaction, two randomly selected agents update their states by applying a deterministic transition function. The goal is to stabilize the system at a desired output property. The main performance objectives in designing such protocols are small number of states per agent and fast stabilization time. We present a fast population protocol for the exact-majority problem, which uses Theta(log n) states (per agent) and stabilizes in O(log^{5/3} n) parallel time (i.e., in O(n log^{5/3} n) interactions) in expectation and with high probability. Alistarh et al. [SODA 2018] showed that exact-majority protocols which stabilize in expected O(n^{1-Omega(1)}) parallel time and have the properties of monotonicity and output dominance require Omega(log n) states. Note that the properties mentioned above are satisfied by all known population protocols for exact majority, including ours. They also showed an O(log^2 n)-time exact-majority protocol with O(log n) states, which, prior to our work, was the fastest exact-majority protocol with polylogarithmic number of states. The standard design framework for majority protocols is based on O(log n) phases and requires that all agents are well synchronized within each phase, leading naturally to upper bounds of the order of log^2 n because of Theta(log n) synchronization time per phase. We show how this framework can be tightened with weak synchronization to break the O(log^2 n) upper bound of previous protocols.
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Petra Berenbrink, Robert Elsässer, Tom Friedetzky, Dominik Kaaser, Peter Kling, and Tomasz Radzik. A Population Protocol for Exact Majority with O(log5/3 n) Stabilization Time and Theta(log n) States. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{berenbrink_et_al:LIPIcs.DISC.2018.10,
  author =	{Berenbrink, Petra and Els\"{a}sser, Robert and Friedetzky, Tom and Kaaser, Dominik and Kling, Peter and Radzik, Tomasz},
  title =	{{A Population Protocol for Exact Majority with O(log5/3 n)  Stabilization Time and Theta(log n) States}},
  booktitle =	{32nd International Symposium on Distributed Computing (DISC 2018)},
  pages =	{10:1--10:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-092-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{121},
  editor =	{Schmid, Ulrich and Widder, Josef},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.10},
  URN =		{urn:nbn:de:0030-drops-97999},
  doi =		{10.4230/LIPIcs.DISC.2018.10},
  annote =	{Keywords: Population Protocols, Randomized Algorithms, Majority}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.136
Efficient Plurality Consensus, Or: the Benefits of Cleaning up from Time to Time

Authors: Petra Berenbrink, Tom Friedetzky, George Giakkoupis, and Peter Kling

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
Plurality consensus considers a network of n nodes, each having one of k opinions. Nodes execute a (randomized) distributed protocol with the goal that all nodes adopt the plurality (the opinion initially supported by the most nodes). Communication is realized via the Gossip (or random phone call) model. A major open question has been whether there is a protocol for the complete graph that converges (w.h.p.) in polylogarithmic time and uses only polylogarithmic memory per node (local memory). We answer this question affirmatively. We propose two protocols that need only mild assumptions on the bias in favor of the plurality. As an example of our results, consider the complete graph and an arbitrarily small constant multiplicative bias in favor of the plurality. Our first protocol achieves plurality consensus in O(log(k)*log(log(n))) rounds using log(k) + Theta(log(log(k))) bits of local memory. Our second protocol achieves plurality consensus in O(log(n)*log(log(n))) rounds using only log(k) + 4 bits of local memory. This disproves a conjecture by Becchetti et al. (SODA'15) implying that any protocol with local memory log(k)+O(1) has worst-case runtime Omega(k). We provide similar bounds for much weaker bias assumptions. At the heart of our protocols lies an undecided state, an idea introduced by Angluin et al. (Distributed Computing'08).
Cite as

Petra Berenbrink, Tom Friedetzky, George Giakkoupis, and Peter Kling. Efficient Plurality Consensus, Or: the Benefits of Cleaning up from Time to Time. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 136:1-136:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{berenbrink_et_al:LIPIcs.ICALP.2016.136,
  author =	{Berenbrink, Petra and Friedetzky, Tom and Giakkoupis, George and Kling, Peter},
  title =	{{Efficient Plurality Consensus, Or: the Benefits of Cleaning up from Time to Time}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{136:1--136:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.136},
  URN =		{urn:nbn:de:0030-drops-62711},
  doi =		{10.4230/LIPIcs.ICALP.2016.136},
  annote =	{Keywords: plurality consensus, voting, majority, distributed, gossip}
}
Document
DOI: 10.4230/LIPIcs.ESA.2016.10
Plurality Consensus in Arbitrary Graphs: Lessons Learned from Load Balancing

Authors: Petra Berenbrink, Tom Friedetzky, Peter Kling, Frederik Mallmann-Trenn, and Chris Wastell

Published in: LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016)

Abstract
We consider plurality consensus in networks of n nodes. Initially, each node has one of k opinions. The nodes execute a (randomized) distributed protocol to agree on the plurality opinion (the opinion initially supported by the most nodes). In certain types of networks the nodes can be quite cheap and simple, and hence one seeks protocols that are not only time efficient but also simple and space efficient. Typically, protocols depend heavily on the employed communication mechanism, which ranges from sequential (only one pair of nodes communicates at any time) to fully parallel (all nodes communicate with all their neighbors at once) and everything in-between. We propose a framework to design protocols for a multitude of communication mechanisms. We introduce protocols that solve the plurality consensus problem and are, with probability 1-o(1), both time and space efficient. Our protocols are based on an interesting relationship between plurality consensus and distributed load balancing. This relationship allows us to design protocols that generalize the state of the art for a large range of problem parameters.
Cite as

Petra Berenbrink, Tom Friedetzky, Peter Kling, Frederik Mallmann-Trenn, and Chris Wastell. Plurality Consensus in Arbitrary Graphs: Lessons Learned from Load Balancing. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{berenbrink_et_al:LIPIcs.ESA.2016.10,
  author =	{Berenbrink, Petra and Friedetzky, Tom and Kling, Peter and Mallmann-Trenn, Frederik and Wastell, Chris},
  title =	{{Plurality Consensus in Arbitrary Graphs: Lessons Learned from Load Balancing}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{10:1--10:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Sankowski, Piotr and Zaroliagis, Christos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.10},
  URN =		{urn:nbn:de:0030-drops-63610},
  doi =		{10.4230/LIPIcs.ESA.2016.10},
  annote =	{Keywords: Plurality Consensus, Distributed Computing, Load Balancing}
}
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