Document

**Published in:** LIPIcs, Volume 217, 25th International Conference on Principles of Distributed Systems (OPODIS 2021)

Let G be a graph on n nodes. In the stochastic population protocol model, a collection of n indistinguishable, resource-limited nodes collectively solve tasks via pairwise interactions. In each interaction, two randomly chosen neighbors first read each other’s states, and then update their local states. A rich line of research has established tight upper and lower bounds on the complexity of fundamental tasks, such as majority and leader election, in this model, when G is a clique. Specifically, in the clique, these tasks can be solved fast, i.e., in n polylog n pairwise interactions, with high probability, using at most polylog n states per node.
In this work, we consider the more general setting where G is an arbitrary regular graph, and present a technique for simulating protocols designed for fully-connected networks in any connected regular graph. Our main result is a simulation that is efficient on many interesting graph families: roughly, the simulation overhead is polylogarithmic in the number of nodes, and quadratic in the conductance of the graph. As a sample application, we show that, in any regular graph with conductance φ, both leader election and exact majority can be solved in φ^{-2} ⋅ n polylog n pairwise interactions, with high probability, using at most φ^{-2} ⋅ polylog n states per node. This shows that there are fast and space-efficient population protocols for leader election and exact majority on graphs with good expansion properties. We believe our results will prove generally useful, as they allow efficient technology transfer between the well-mixed (clique) case, and the under-explored spatial setting.

Dan Alistarh, Rati Gelashvili, and Joel Rybicki. Fast Graphical Population Protocols. In 25th International Conference on Principles of Distributed Systems (OPODIS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 217, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{alistarh_et_al:LIPIcs.OPODIS.2021.14, author = {Alistarh, Dan and Gelashvili, Rati and Rybicki, Joel}, title = {{Fast Graphical Population Protocols}}, booktitle = {25th International Conference on Principles of Distributed Systems (OPODIS 2021)}, pages = {14:1--14:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-219-8}, ISSN = {1868-8969}, year = {2022}, volume = {217}, editor = {Bramas, Quentin and Gramoli, Vincent and Milani, Alessia}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2021.14}, URN = {urn:nbn:de:0030-drops-157897}, doi = {10.4230/LIPIcs.OPODIS.2021.14}, annote = {Keywords: population protocols, leader election, exact majority, graphs} }

Document

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

This paper gives tight logarithmic lower bounds on the solo step complexity of leader election in an asynchronous shared-memory model with single-writer multi-reader (SWMR) registers, for both deterministic and randomized obstruction-free algorithms. The approach extends to lower bounds for deterministic and randomized obstruction-free algorithms using multi-writer registers under bounded write concurrency, showing a trade-off between the solo step complexity of a leader election algorithm, and the worst-case number of stalls incurred by a processor in an execution.

Dan Alistarh, Rati Gelashvili, and Giorgi Nadiradze. Lower Bounds for Shared-Memory Leader Election Under Bounded Write Contention. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 4:1-4:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{alistarh_et_al:LIPIcs.DISC.2021.4, author = {Alistarh, Dan and Gelashvili, Rati and Nadiradze, Giorgi}, title = {{Lower Bounds for Shared-Memory Leader Election Under Bounded Write Contention}}, booktitle = {35th International Symposium on Distributed Computing (DISC 2021)}, pages = {4:1--4:17}, 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.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2021.4}, URN = {urn:nbn:de:0030-drops-148063}, doi = {10.4230/LIPIcs.DISC.2021.4}, annote = {Keywords: Lower Bounds, Leader Election, Shared-Memory} }

Document

Brief Announcement

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

Let G be a graph on n nodes. In the stochastic population protocol model, a collection of n indistinguishable, resource-limited nodes collectively solve tasks via pairwise interactions. In each interaction, two randomly chosen neighbors first read each other’s states, and then update their local states. A rich line of research has established tight upper and lower bounds on the complexity of fundamental tasks, such as majority and leader election, in this model, when G is a clique. Specifically, in the clique, these tasks can be solved fast, i.e., in n polylog n pairwise interactions, with high probability, using at most polylog n states per node.
In this work, we consider the more general setting where G is an arbitrary graph, and present a technique for simulating protocols designed for fully-connected networks in any connected regular graph. Our main result is a simulation that is efficient on many interesting graph families: roughly, the simulation overhead is polylogarithmic in the number of nodes, and quadratic in the conductance of the graph. As an example, this implies that, in any regular graph with conductance φ, both leader election and exact majority can be solved in φ^{-2} ⋅ n polylog n pairwise interactions, with high probability, using at most φ^{-2} ⋅ polylog n states per node. This shows that there are fast and space-efficient population protocols for leader election and exact majority on graphs with good expansion properties.

Dan Alistarh, Rati Gelashvili, and Joel Rybicki. Brief Announcement: Fast Graphical Population Protocols. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 43:1-43:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{alistarh_et_al:LIPIcs.DISC.2021.43, author = {Alistarh, Dan and Gelashvili, Rati and Rybicki, Joel}, title = {{Brief Announcement: Fast Graphical Population Protocols}}, booktitle = {35th International Symposium on Distributed Computing (DISC 2021)}, pages = {43:1--43:4}, 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.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2021.43}, URN = {urn:nbn:de:0030-drops-148451}, doi = {10.4230/LIPIcs.DISC.2021.43}, annote = {Keywords: population protocols, leader election, majority} }

Document

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

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.

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)

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@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.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

Brief Announcement

**Published in:** LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017)

Contrary to common belief, a recent work by Ellen, Gelashvili, Shavit, and Zhu has shown that computability does not require multicore architectures to support "strong" synchronization instructions like compare-and-swap, as opposed to combinations of "weaker" instructions like decrement and multiply. However, this is the status quo, and in turn, most efficient concurrent data-structures heavily rely on compare-and-swap (e.g. for swinging pointers).
We show that this need not be the case, by designing and implementing a concurrent linearizable Log data-structure (also known as a History object), supporting two operations: append(item), which appends the item to the log, and get-log(), which returns the appended items so far, in order. Readers are wait-free and writers are lock-free, hence this data-structure can be used in a lock-free universal construction to implement any concurrent object with a given sequential specification. Our implementation uses atomic read, xor, decrement, and fetch-and-increment instructions supported on X86 architectures, and provides similar performance to a compare-and-swap-based solution on today's hardware. This raises a fundamental question about minimal set of synchronization instructions that the architectures have to support.

Rati Gelashvili, Idit Keidar, Alexander Spiegelman, and Roger Wattenhofer. Brief Announcement: Towards Reduced Instruction Sets for Synchronization. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 53:1-53:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{gelashvili_et_al:LIPIcs.DISC.2017.53, author = {Gelashvili, Rati and Keidar, Idit and Spiegelman, Alexander and Wattenhofer, Roger}, title = {{Brief Announcement: Towards Reduced Instruction Sets for Synchronization}}, booktitle = {31st International Symposium on Distributed Computing (DISC 2017)}, pages = {53:1--53:4}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-053-8}, ISSN = {1868-8969}, year = {2017}, volume = {91}, editor = {Richa, Andr\'{e}a}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.53}, URN = {urn:nbn:de:0030-drops-80201}, doi = {10.4230/LIPIcs.DISC.2017.53}, annote = {Keywords: Consensus hierarchy, universal construction, synchronization instruction.} }

Document

**Published in:** LIPIcs, Volume 34, 31st International Symposium on Computational Geometry (SoCG 2015)

The Restricted Isometry Property (RIP) is a fundamental property of a matrix which enables sparse recovery. Informally, an m x n matrix satisfies RIP of order k for the L_p norm, if |Ax|_p is approximately |x|_p for every x with at most k non-zero coordinates.
For every 1 <= p < infty we obtain almost tight bounds on the minimum number of rows m necessary for the RIP property to hold. Prior to this work, only the cases p = 1, 1 + 1/log(k), and 2 were studied. Interestingly, our results show that the case p=2 is a "singularity" point: the optimal number of rows m is Theta(k^p) for all p in [1, infty)-{2}, as opposed to Theta(k) for k=2.
We also obtain almost tight bounds for the column sparsity of RIP matrices and discuss implications of our results for the Stable Sparse Recovery problem.

Zeyuan Allen-Zhu, Rati Gelashvili, and Ilya Razenshteyn. Restricted Isometry Property for General p-Norms. In 31st International Symposium on Computational Geometry (SoCG 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 34, pp. 451-460, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{allenzhu_et_al:LIPIcs.SOCG.2015.451, author = {Allen-Zhu, Zeyuan and Gelashvili, Rati and Razenshteyn, Ilya}, title = {{Restricted Isometry Property for General p-Norms}}, booktitle = {31st International Symposium on Computational Geometry (SoCG 2015)}, pages = {451--460}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-83-5}, ISSN = {1868-8969}, year = {2015}, volume = {34}, editor = {Arge, Lars and Pach, J\'{a}nos}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SOCG.2015.451}, URN = {urn:nbn:de:0030-drops-51273}, doi = {10.4230/LIPIcs.SOCG.2015.451}, annote = {Keywords: compressive sensing, dimension reduction, linear algebra, high-dimensional geometry} }

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