5 Search Results for "Zhu, Leqi"


Document
Extension-Based Proofs for Synchronous Message Passing

Authors: Yilun Sheng and Faith Ellen

Published in: LIPIcs, Volume 209, 35th International Symposium on Distributed Computing (DISC 2021)


Abstract
There is no wait-free algorithm that solves k-set agreement among n ≥ k+1 processes in asynchronous systems where processes communicate using only registers. However, proofs of this result for k ≥ 2 are complicated and involve topological reasoning. To explain why such sophisticated arguments are necessary, Alistarh, Aspnes, Ellen, Gelashvili, and Zhu recently introduced extension-based proofs, which generalize valency arguments, and proved that there are no extension-based proofs of this result. In the synchronous message passing model, k-set agreement is solvable, but there is a lower bound of t rounds for any k-set agreement algorithm among n > kt processes when at most k processes can crash each round. The proof of this result for k ≥ 2 is also a complicated topological argument. We define a notion of extension-based proofs for this model and we show there are no extension-based proofs that t rounds are necessary for any k-set agreement algorithm among n = kt+1 processes, for k ≥ 2 and t > 2, when at most k processes can crash each round. In particular, our result shows that no valency argument can prove this lower bound.

Cite as

Yilun Sheng and Faith Ellen. Extension-Based Proofs for Synchronous Message Passing. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 36:1-36:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Copy BibTex To Clipboard

@InProceedings{sheng_et_al:LIPIcs.DISC.2021.36,
  author =	{Sheng, Yilun and Ellen, Faith},
  title =	{{Extension-Based Proofs for Synchronous Message Passing}},
  booktitle =	{35th International Symposium on Distributed Computing (DISC 2021)},
  pages =	{36:1--36:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-210-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{209},
  editor =	{Gilbert, Seth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2021.36},
  URN =		{urn:nbn:de:0030-drops-148380},
  doi =		{10.4230/LIPIcs.DISC.2021.36},
  annote =	{Keywords: Set agreement, lower bounds, valency arguments}
}
Document
Locally Solvable Tasks and the Limitations of Valency Arguments

Authors: Hagit Attiya, Armando Castañeda, and Sergio Rajsbaum

Published in: LIPIcs, Volume 184, 24th International Conference on Principles of Distributed Systems (OPODIS 2020)


Abstract
An elegant strategy for proving impossibility results in distributed computing was introduced in the celebrated FLP consensus impossibility proof. This strategy is local in nature as at each stage, one configuration of a hypothetical protocol for consensus is considered, together with future valencies of possible extensions. This proof strategy has been used in numerous situations related to consensus, leading one to wonder why it has not been used in impossibility results of two other well-known tasks: set agreement and renaming. This paper provides an explanation of why impossibility proofs of these tasks have been of a global nature. It shows that a protocol can always solve such tasks locally, in the following sense. Given a configuration and all its future valencies, if a single successor configuration is selected, then the protocol can reveal all decisions in this branch of executions, satisfying the task specification. This result is shown for both set agreement and renaming, implying that there are no local impossibility proofs for these tasks.

Cite as

Hagit Attiya, Armando Castañeda, and Sergio Rajsbaum. Locally Solvable Tasks and the Limitations of Valency Arguments. In 24th International Conference on Principles of Distributed Systems (OPODIS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 184, pp. 18:1-18:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Copy BibTex To Clipboard

@InProceedings{attiya_et_al:LIPIcs.OPODIS.2020.18,
  author =	{Attiya, Hagit and Casta\~{n}eda, Armando and Rajsbaum, Sergio},
  title =	{{Locally Solvable Tasks and the Limitations of Valency Arguments}},
  booktitle =	{24th International Conference on Principles of Distributed Systems (OPODIS 2020)},
  pages =	{18:1--18:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-176-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{184},
  editor =	{Bramas, Quentin and Oshman, Rotem and Romano, Paolo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2020.18},
  URN =		{urn:nbn:de:0030-drops-135037},
  doi =		{10.4230/LIPIcs.OPODIS.2020.18},
  annote =	{Keywords: Wait-freedom, Set agreement, Weak symmetry breaking, Impossibility proofs}
}
Document
Space Lower Bounds for the Signal Detection Problem

Authors: Faith Ellen, Rati Gelashvili, Philipp Woelfel, and Leqi Zhu

Published in: LIPIcs, Volume 126, 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)


Abstract
Many shared memory algorithms have to deal with the problem of determining whether the value of a shared object has changed in between two successive accesses of that object by a process when the responses from both are the same. Motivated by this problem, we define the signal detection problem, which can be studied on a purely combinatorial level. Consider a system with n+1 processes consisting of n readers and one signaller. The processes communicate through a shared blackboard that can store a value from a domain of size m. Processes are scheduled by an adversary. When scheduled, a process reads the blackboard, modifies its contents arbitrarily, and, provided it is a reader, returns a Boolean value. A reader must return true if the signaller has taken a step since the reader’s preceding step; otherwise it must return false. Intuitively, in a system with n processes, signal detection should require at least n bits of shared information, i.e., m >= 2^n. But a proof of this conjecture remains elusive. We prove a lower bound of m >= n^2, as well as a tight lower bound of m >= 2^n for two restricted versions of the problem, where the processes are oblivious or where the signaller always resets the blackboard to the same fixed value. We also consider a one-shot version of the problem, where each reader takes at most two steps. In this case, we prove that it is necessary and sufficient that the blackboard can store m=n+1 values.

Cite as

Faith Ellen, Rati Gelashvili, Philipp Woelfel, and Leqi Zhu. Space Lower Bounds for the Signal Detection Problem. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 26:1-26:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Copy BibTex To Clipboard

@InProceedings{ellen_et_al:LIPIcs.STACS.2019.26,
  author =	{Ellen, Faith and Gelashvili, Rati and Woelfel, Philipp and Zhu, Leqi},
  title =	{{Space Lower Bounds for the Signal Detection Problem}},
  booktitle =	{36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
  pages =	{26:1--26:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-100-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{126},
  editor =	{Niedermeier, Rolf and Paul, Christophe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.26},
  URN =		{urn:nbn:de:0030-drops-102654},
  doi =		{10.4230/LIPIcs.STACS.2019.26},
  annote =	{Keywords: Signal detection, ABA problem, space complexity, lower bound}
}
Document
Allocate-On-Use Space Complexity of Shared-Memory Algorithms

Authors: James Aspnes, Bernhard Haeupler, Alexander Tong, and Philipp Woelfel

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


Abstract
Many fundamental problems in shared-memory distributed computing, including mutual exclusion [James E. Burns and Nancy A. Lynch, 1993], consensus [Leqi Zhu, 2016], and implementations of many sequential objects [Prasad Jayanti et al., 2000], are known to require linear space in the worst case. However, these lower bounds all work by constructing particular executions for any given algorithm that may be both very long and very improbable. The significance of these bounds is justified by an assumption that any space that is used in some execution must be allocated for all executions. This assumption is not consistent with the storage allocation mechanisms of actual practical systems. We consider the consequences of adopting a per-execution approach to space complexity, where an object only counts toward the space complexity of an execution if it is used in that execution. This allows us to show that many known randomized algorithms for fundamental problems in shared-memory distributed computing have expected space complexity much lower than the worst-case lower bounds, and that many algorithms that are adaptive in time complexity can also be made adaptive in space complexity. For the specific problem of mutual exclusion, we develop a new algorithm that illustrates an apparent trade-off between low expected space complexity and low expected RMR complexity. Whether this trade-off is necessary is an open problem. For some applications, it may be helpful to pay only for objects that are updated, as opposed to those that are merely read. We give a data structure that requires no space to represent objects that are not updated at the cost of a small overhead on those that are.

Cite as

James Aspnes, Bernhard Haeupler, Alexander Tong, and Philipp Woelfel. Allocate-On-Use Space Complexity of Shared-Memory Algorithms. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Copy BibTex To Clipboard

@InProceedings{aspnes_et_al:LIPIcs.DISC.2018.8,
  author =	{Aspnes, James and Haeupler, Bernhard and Tong, Alexander and Woelfel, Philipp},
  title =	{{Allocate-On-Use Space Complexity of Shared-Memory Algorithms}},
  booktitle =	{32nd International Symposium on Distributed Computing (DISC 2018)},
  pages =	{8:1--8:17},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.8},
  URN =		{urn:nbn:de:0030-drops-97974},
  doi =		{10.4230/LIPIcs.DISC.2018.8},
  annote =	{Keywords: Space complexity, memory allocation, mutual exclusion}
}
Document
Atomic Snapshots from Small Registers

Authors: Leqi Zhu and Faith Ellen

Published in: LIPIcs, Volume 46, 19th International Conference on Principles of Distributed Systems (OPODIS 2015)


Abstract
Existing n-process implementations of atomic snapshots from registers use large registers. We consider the problem of implementing an m-component snapshot from small, Theta(log(n))-bit registers. A natural solution is to consider simulating the large registers. Doing so straightforwardly can significantly increase the step complexity. We introduce the notion of an interruptible read and show how it can reduce the step complexity of simulating the large registers in the snapshot of Afek et al. In particular, we show how to modify a recent large register simulation to support interruptible reads. Using this modified simulation, the step complexity of UPDATE and SCAN changes from Theta(n*m) to Theta(n*m+m*w), instead of Theta(n*m*w), if each component of the snapshot consists of Theta(w*log(n)) bits. We also show how to modify a limited-use snapshot to use small registers when the number of UPDATE operations is in n^{O(1)}. In this case, we change the step complexity of UPDATE from Theta((log(n))^3) to O(w + (log(n))^2*log(m)) and the step complexity of SCAN from Theta(log(n)) to O(m*w + log(n)).

Cite as

Leqi Zhu and Faith Ellen. Atomic Snapshots from Small Registers. In 19th International Conference on Principles of Distributed Systems (OPODIS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 46, pp. 17:1-17:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


Copy BibTex To Clipboard

@InProceedings{zhu_et_al:LIPIcs.OPODIS.2015.17,
  author =	{Zhu, Leqi and Ellen, Faith},
  title =	{{Atomic Snapshots from Small Registers}},
  booktitle =	{19th International Conference on Principles of Distributed Systems (OPODIS 2015)},
  pages =	{17:1--17:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-98-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{46},
  editor =	{Anceaume, Emmanuelle and Cachin, Christian and Potop-Butucaru, Maria},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2015.17},
  URN =		{urn:nbn:de:0030-drops-66084},
  doi =		{10.4230/LIPIcs.OPODIS.2015.17},
  annote =	{Keywords: atomic snapshot, limited-use snapshot, small registers, simulation}
}
  • Refine by Author
  • 3 Ellen, Faith
  • 2 Woelfel, Philipp
  • 2 Zhu, Leqi
  • 1 Aspnes, James
  • 1 Attiya, Hagit
  • Show More...

  • Refine by Classification
  • 3 Theory of computation → Distributed algorithms
  • 3 Theory of computation → Distributed computing models
  • 1 Computing methodologies → Concurrent algorithms
  • 1 Computing methodologies → Distributed algorithms
  • 1 Computing methodologies → Shared memory algorithms
  • Show More...

  • Refine by Keyword
  • 2 Set agreement
  • 1 ABA problem
  • 1 Impossibility proofs
  • 1 Signal detection
  • 1 Space complexity
  • Show More...

  • Refine by Type
  • 5 document

  • Refine by Publication Year
  • 2 2021
  • 1 2016
  • 1 2018
  • 1 2019

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail