3 Search Results for "Winkler, Kyrill"


Document
Stabilizing Consensus Is Impossible in Lossy Iterated Immediate Snapshot Models

Authors: Stephan Felber and Hugo Rincon Galeana

Published in: LIPIcs, Volume 324, 28th International Conference on Principles of Distributed Systems (OPODIS 2024)


Abstract
A substantial portion of distributed computing research is dedicated to terminating problems like consensus and similar agreement problems. However, non-terminating problems have been intensively studied in the context of self-stabilizing distributed algorithms, where processes may start from arbitrary initial states and can tolerate arbitrary transient faults. In between lie stabilizing problems, where the processes start from a well-defined initial state, but do not need to decide irrevocably and are allowed to change their decision finitely often until a stable decision is eventually reached. Stabilizing consensus has been studied within the context of synchronous message adversaries. In particular, Charron-Bost and Moran showed that a necessary condition for stabilizing consensus is the existence of at least one process that reaches all others infinitely often (a perpetual broadcaster). However, it was left open whether this is also a sufficient condition for solving stabilizing consensus. In this paper, we introduce the novel Delayed Lossy-Link (DLL) model, and the Lossy Iterated Immediate Snapshot Model (LIIS), for which we show stabilizing consensus to be impossible. The DLL model is introduced as a variant of the well-known Lossy-Link model, which admits silence periods of arbitrary but finite length. The LIIS model is a variant of the Iterated Immediate Snapshot (IIS), model which admits finite length periods of at most f omission faults per layer. In particular, we show that stabilizing consensus is impossible even when f = 1. Our results show that even in a model with very strong connectivity, namely, the Iterated Immediate Snapshot (IIS) model, a single omission fault per layer effectively disables stabilizing consensus. Furthermore, since the DLL model always has a perpetual broadcaster, the mere existence of a perpetual broadcaster, even in a crash-free setting, is not sufficient for solving stabilizing consensus, negatively answering the open question posed by Charron-Bost and Moran.

Cite as

Stephan Felber and Hugo Rincon Galeana. Stabilizing Consensus Is Impossible in Lossy Iterated Immediate Snapshot Models. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 18:1-18:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{felber_et_al:LIPIcs.OPODIS.2024.18,
  author =	{Felber, Stephan and Rincon Galeana, Hugo},
  title =	{{Stabilizing Consensus Is Impossible in Lossy Iterated Immediate Snapshot Models}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{18:1--18:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.18},
  URN =		{urn:nbn:de:0030-drops-225544},
  doi =		{10.4230/LIPIcs.OPODIS.2024.18},
  annote =	{Keywords: distributed systems, dynamic networks, dynamic graphs, message adversaries, stabilizing consensus, asynchronous message passing}
}
Document
The Time Complexity of Consensus Under Oblivious Message Adversaries

Authors: Kyrill Winkler, Ami Paz, Hugo Rincon Galeana, Stefan Schmid, and Ulrich Schmid

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)


Abstract
We study the problem of solving consensus in synchronous directed dynamic networks, in which communication is controlled by an oblivious message adversary that picks the communication graph to be used in a round from a fixed set of graphs 𝐃 arbitrarily. In this fundamental model, determining consensus solvability and designing efficient consensus algorithms is surprisingly difficult. Enabled by a decision procedure that is derived from a well-established previous consensus solvability characterization for a given set 𝐃, we study, for the first time, the time complexity of solving consensus in this model: We provide both upper and lower bounds for this time complexity, and also relate it to the number of iterations required by the decision procedure. Among other results, we find that reaching consensus under an oblivious message adversary can take exponentially longer than both deciding consensus solvability and broadcasting the input value of some unknown process to all other processes.

Cite as

Kyrill Winkler, Ami Paz, Hugo Rincon Galeana, Stefan Schmid, and Ulrich Schmid. The Time Complexity of Consensus Under Oblivious Message Adversaries. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 100:1-100:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{winkler_et_al:LIPIcs.ITCS.2023.100,
  author =	{Winkler, Kyrill and Paz, Ami and Rincon Galeana, Hugo and Schmid, Stefan and Schmid, Ulrich},
  title =	{{The Time Complexity of Consensus Under Oblivious Message Adversaries}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{100:1--100:28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.100},
  URN =		{urn:nbn:de:0030-drops-176030},
  doi =		{10.4230/LIPIcs.ITCS.2023.100},
  annote =	{Keywords: dynamic networks, oblivious message adversaries, consensus, time complexity}
}
Document
A Characterization of Consensus Solvability for Closed Message Adversaries

Authors: Kyrill Winkler, Ulrich Schmid, and Yoram Moses

Published in: LIPIcs, Volume 153, 23rd International Conference on Principles of Distributed Systems (OPODIS 2019)


Abstract
Distributed computations in a synchronous system prone to message loss can be modeled as a game between a (deterministic) distributed algorithm versus an omniscient message adversary. The latter determines, for each round, the directed communication graph that specifies which messages can reach their destination. Message adversary definitions range from oblivious ones, which pick the communication graphs arbitrarily from a given set of candidate graphs, to general message adversaries, which are specified by the set of sequences of communication graphs (called admissible communication patterns) that they may generate. This paper provides a complete characterization of consensus solvability for closed message adversaries, where every inadmissible communication pattern has a finite prefix that makes all (infinite) extensions of this prefix inadmissible. Whereas every oblivious message adversary is closed, there are also closed message adversaries that are not oblivious. We provide a tight non-topological, purely combinatorial characterization theorem, which reduces consensus solvability to a simple condition on prefixes of the communication patterns. Our result not only non-trivially generalizes the known combinatorial characterization of the consensus solvability for oblivious message adversaries by Coulouma, Godard, and Peters (Theor. Comput. Sci., 2015), but also provides the first combinatorial characterization for this important class of message adversaries that is formulated directly on the prefixes of the communication patterns.

Cite as

Kyrill Winkler, Ulrich Schmid, and Yoram Moses. A Characterization of Consensus Solvability for Closed Message Adversaries. In 23rd International Conference on Principles of Distributed Systems (OPODIS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 153, pp. 17:1-17:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Copy BibTex To Clipboard

@InProceedings{winkler_et_al:LIPIcs.OPODIS.2019.17,
  author =	{Winkler, Kyrill and Schmid, Ulrich and Moses, Yoram},
  title =	{{A Characterization of Consensus Solvability for Closed Message Adversaries}},
  booktitle =	{23rd International Conference on Principles of Distributed Systems (OPODIS 2019)},
  pages =	{17:1--17:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-133-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{153},
  editor =	{Felber, Pascal and Friedman, Roy and Gilbert, Seth and Miller, Avery},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2019.17},
  URN =		{urn:nbn:de:0030-drops-118038},
  doi =		{10.4230/LIPIcs.OPODIS.2019.17},
  annote =	{Keywords: Dynamic networks, Consensus, Message Adversary}
}
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