9 Search Results for "Naor, Oded"

Document
DOI: 10.4230/LIPIcs.DISC.2023.26
Cordial Miners: Fast and Efficient Consensus for Every Eventuality

Authors: Idit Keidar, Oded Naor, Ouri Poupko, and Ehud Shapiro

Published in: LIPIcs, Volume 281, 37th International Symposium on Distributed Computing (DISC 2023)

Abstract
Cordial Miners are a family of efficient Byzantine Atomic Broadcast protocols, with instances for asynchrony and eventual synchrony. They improve the latency of state-of-the-art DAG-based protocols by almost 2× and achieve optimal good-case complexity of O(n) by forgoing Reliable Broadcast as a building block. Rather, Cordial Miners use the blocklace - a partially-ordered counterpart of the totally-ordered blockchain data structure - to implement the three algorithmic components of consensus: Dissemination, equivocation-exclusion, and ordering.
Cite as

Idit Keidar, Oded Naor, Ouri Poupko, and Ehud Shapiro. Cordial Miners: Fast and Efficient Consensus for Every Eventuality. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 26:1-26:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{keidar_et_al:LIPIcs.DISC.2023.26,
  author =	{Keidar, Idit and Naor, Oded and Poupko, Ouri and Shapiro, Ehud},
  title =	{{Cordial Miners: Fast and Efficient Consensus for Every Eventuality}},
  booktitle =	{37th International Symposium on Distributed Computing (DISC 2023)},
  pages =	{26:1--26:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-301-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{281},
  editor =	{Oshman, Rotem},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.26},
  URN =		{urn:nbn:de:0030-drops-191525},
  doi =		{10.4230/LIPIcs.DISC.2023.26},
  annote =	{Keywords: Byzantine Fault Tolerance, State Machine Replication, DAG, Consensus, Blockchain, Blocklace, Cordial Dissemination}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2023.47
Brief Announcement: Grassroots Distributed Systems: Concept, Examples, Implementation and Applications

Authors: Ehud Shapiro

Published in: LIPIcs, Volume 281, 37th International Symposium on Distributed Computing (DISC 2023)

Abstract
Informally, a distributed system is grassroots if it is permissionless and can have autonomous, independently-deployed instances - geographically and over time - that may interoperate voluntarily once interconnected. More formally, in a grassroots system the set of all correct behaviors of a set of agents P is strictly included in the set of the correct behaviors of P when they are embedded within a larger set of agents P' ⊃ P. Grassroots systems are potentially important as they may allow communities to conduct their social, economic, civic, and political lives in the digital realm solely using their members' networked computing devices (e.g., smartphones), free of third-party control, surveillance, manipulation, coercion, or rent seeking (e.g., by global digital platforms such as Facebook or Bitcoin). Client-server/cloud computing systems are not grassroots, and neither are systems designed to have a single global instance (Bitcoin/Ethereum with hardwired seed miners/bootnodes), and systems that rely on a single global data structure (IPFS, DHTs). An example grassroots system would be a serverless smartphone-based social network supporting multiple independently-budding communities that can merge when a member of one community becomes also a member of another. Here, we formalize the notion of grassroots distributed systems; describe a grassroots dissemination protocol for the model of asynchrony and argue its safety, liveness, and being grassroots; extend the implementation to mobile (address-changing) devices that communicate via an unreliable network (e.g. smartphones using UDP); and discuss how grassroots dissemination can realize grassroots social networking and grassroots cryptocurrencies. The mathematical construction employs distributed multiagent transition systems to define the notions of grassroots protocols, to specify the grassroots dissemination protocols, and to prove their correctness. The protocols use the blocklace - a distributed, partially-ordered counterpart of the replicated, totally-ordered blockchain.
Cite as

Ehud Shapiro. Brief Announcement: Grassroots Distributed Systems: Concept, Examples, Implementation and Applications. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 47:1-47:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{shapiro:LIPIcs.DISC.2023.47,
  author =	{Shapiro, Ehud},
  title =	{{Brief Announcement: Grassroots Distributed Systems: Concept, Examples, Implementation and Applications}},
  booktitle =	{37th International Symposium on Distributed Computing (DISC 2023)},
  pages =	{47:1--47:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-301-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{281},
  editor =	{Oshman, Rotem},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.47},
  URN =		{urn:nbn:de:0030-drops-191735},
  doi =		{10.4230/LIPIcs.DISC.2023.47},
  annote =	{Keywords: Grassroots Distributed Systems, Dissemination Protocol, Multiagent Transition Systems, Blocklace, Cordial Dissemination}
}
Document
DOI: 10.4230/OASIcs.Tokenomics.2022.6
Maximal Extractable Value (MEV) Protection on a DAG

Authors: Dahlia Malkhi and Pawel Szalachowski

Published in: OASIcs, Volume 110, 4th International Conference on Blockchain Economics, Security and Protocols (Tokenomics 2022)

Abstract
Many cryptocurrency platforms are vulnerable to Maximal Extractable Value (MEV) attacks [Daian et al., 2020], where a malicious consensus leader can inject transactions or change the order of user transactions to maximize its profit. A promising line of research in MEV mitigation is to enhance the Byzantine fault tolerance (BFT) consensus core of blockchains by new functionalities, like hiding transaction contents, such that malicious parties cannot analyze and exploit them until they are ordered. An orthogonal line of research demonstrates excellent performance for BFT protocols designed around Directed Acyclic Graphs (DAG). They provide high throughput by keeping high network utilization, decoupling transactions' dissemination from their metadata ordering, and encoding consensus logic efficiently over a DAG representing a causal ordering of disseminated messages. This paper explains how to combine these two advances. It introduces a DAG-based protocol called Fino, that integrates MEV-resistance features into DAG-based BFT without delaying the steady spreading of transactions by the DAG transport and with zero message overhead. The scheme operates without complex secret share verifiability or recoverability, and avoids costly threshold encryption.
Cite as

Dahlia Malkhi and Pawel Szalachowski. Maximal Extractable Value (MEV) Protection on a DAG. In 4th International Conference on Blockchain Economics, Security and Protocols (Tokenomics 2022). Open Access Series in Informatics (OASIcs), Volume 110, pp. 6:1-6:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{malkhi_et_al:OASIcs.Tokenomics.2022.6,
  author =	{Malkhi, Dahlia and Szalachowski, Pawel},
  title =	{{Maximal Extractable Value (MEV) Protection on a DAG}},
  booktitle =	{4th International Conference on Blockchain Economics, Security and Protocols (Tokenomics 2022)},
  pages =	{6:1--6:17},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-274-7},
  ISSN =	{2190-6807},
  year =	{2023},
  volume =	{110},
  editor =	{Amoussou-Guenou, Yackolley and Kiayias, Aggelos and Verdier, Marianne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.Tokenomics.2022.6},
  URN =		{urn:nbn:de:0030-drops-184231},
  doi =		{10.4230/OASIcs.Tokenomics.2022.6},
  annote =	{Keywords: DAG, MEV, consensus, BFT}
}
Document
DOI: 10.4230/LIPIcs.DISC.2022.29
On Payment Channels in Asynchronous Money Transfer Systems

Authors: Oded Naor and Idit Keidar

Published in: LIPIcs, Volume 246, 36th International Symposium on Distributed Computing (DISC 2022)

Abstract
Money transfer is an abstraction that realizes the core of cryptocurrencies. It has been shown that, contrary to common belief, money transfer in the presence of Byzantine faults can be implemented in asynchronous networks and does not require consensus. Nonetheless, existing implementations of money transfer still require a quadratic message complexity per payment, making attempts to scale hard. In common blockchains, such as Bitcoin and Ethereum, this cost is mitigated by payment channels implemented as a second layer on top of the blockchain allowing to make many off-chain payments between two users who share a channel. Such channels require only on-chain transactions for channel opening and closing, while the intermediate payments are done off-chain with constant message complexity. But payment channels in-use today require synchrony; therefore, they are inadequate for asynchronous money transfer systems. In this paper, we provide a series of possibility and impossibility results for payment channels in asynchronous money transfer systems. We first prove a quadratic lower bound on the message complexity of on-chain transfers. Then, we explore two types of payment channels, unidirectional and bidirectional. We define them as shared memory abstractions and prove that in certain cases they can be implemented as a second layer on top of an asynchronous money transfer system whereas in other cases it is impossible.
Cite as

Oded Naor and Idit Keidar. On Payment Channels in Asynchronous Money Transfer Systems. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 29:1-29:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{naor_et_al:LIPIcs.DISC.2022.29,
  author =	{Naor, Oded and Keidar, Idit},
  title =	{{On Payment Channels in Asynchronous Money Transfer Systems}},
  booktitle =	{36th International Symposium on Distributed Computing (DISC 2022)},
  pages =	{29:1--29:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-255-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{246},
  editor =	{Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.29},
  URN =		{urn:nbn:de:0030-drops-172201},
  doi =		{10.4230/LIPIcs.DISC.2022.29},
  annote =	{Keywords: Blockchains, Asynchrony, Byzantine faults, Payment channels}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.28
A Sublinear Local Access Implementation for the Chinese Restaurant Process

Authors: Peter Mörters, Christian Sohler, and Stefan Walzer

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)

Abstract
The Chinese restaurant process is a stochastic process closely related to the Dirichlet process that groups sequentially arriving objects into a variable number of classes, such that within each class objects are cyclically ordered. A popular description involves a restaurant, where customers arrive one by one and either sit down next to a randomly chosen customer at one of the existing tables or open a new table. The full state of the process after n steps is given by a permutation of the n objects and cannot be represented in sublinear space. In particular, if we only need specific information about a few objects or classes it would be preferable to obtain the answers without simulating the process completely. A recent line of research [Oded Goldreich et al., 2010; Moni Naor and Asaf Nussboim, 2007; Amartya Shankha Biswas et al., 2020; Guy Even et al., 2021] attempts to provide access to huge random objects without fully instantiating them. Such local access implementations provide answers to a sequence of queries about the random object, following the same distribution as if the object was fully generated. In this paper, we provide a local access implementation for a generalization of the Chinese restaurant process described above. Our implementation can be used to answer any sequence of adaptive queries about class affiliation of objects, number and sizes of classes at any time, position of elements within a class, or founding time of a class. The running time per query is polylogarithmic in the total size of the object, with high probability. Our approach relies on some ideas from the recent local access implementation for preferential attachment trees by Even et al. [Guy Even et al., 2021]. Such trees are related to the Chinese restaurant process in the sense that both involve a "rich-get-richer" phenomenon. A novel ingredient in our implementation is to embed the process in continuous time, in which the evolution of the different classes becomes stochastically independent [Joyce and Tavaré, 1987]. This independence is used to keep the probabilistic structure manageable even if many queries have already been answered. As similar embeddings are available for a wide range of urn processes [Krishna B. Athreya and Samuel Karlin, 1968], we believe that our approach may be applicable more generally. Moreover, local access implementations for birth and death processes that we encounter along the way may be of independent interest.
Cite as

Peter Mörters, Christian Sohler, and Stefan Walzer. A Sublinear Local Access Implementation for the Chinese Restaurant Process. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 28:1-28:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{morters_et_al:LIPIcs.APPROX/RANDOM.2022.28,
  author =	{M\"{o}rters, Peter and Sohler, Christian and Walzer, Stefan},
  title =	{{A Sublinear Local Access Implementation for the Chinese Restaurant Process}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{28:1--28:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.28},
  URN =		{urn:nbn:de:0030-drops-171500},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.28},
  annote =	{Keywords: Chinese restaurant process, Dirichlet process, sublinear time algorithm, random recursive tree, random permutation, random partition, Ewens distribution, simulation, local access implementation, continuous time embedding}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.OPODIS.2020.2
Byzantine Agreement and SMR with Sub-Quadratic Message Complexity (Invited Talk)

Authors: Idit Keidar

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

Abstract
Byzantine Agreement (BA) has been studied for four decades by now, but until recently, has been considered at a fairly small scale. In recent years, however, we begin to see practical use-cases of BA in large-scale systems, which motivates a push for reduced communication complexity. Dolev and Reischuk’s well-known lower bound stipulates that any deterministic algorithm requires Ω(n²) communication in the worst-case, and until fairly recently, almost all randomized algorithms have had at least quadratic complexity as well. This talk will present two new algorithms breaking this barrier. The first part of the talk will consider a fully asynchronous setting, focusing on randomized BA whose safety and liveness guarantees hold with high probability. It will present the first asynchronous Byzantine Agreement algorithm with sub-quadratic communication complexity. This algorithm exploits VRF-based committee sampling, which it adapts for the asynchronous model. The second part of the talk will consider the eventually synchronous model, where BA and State Machine Replication (SMR) can be solved with deterministic safety and liveness guarantees. In this context, randomization is used in order to reduce the expected communication complexity. The talk will present an algorithm for round synchronization, which is a building block for BA and SMR and constitutes the main performance bottleneck therein. It will present an algorithm that, for the first time, achieves round synchronization with expected linear message complexity and expected constant latency. Existing protocols can use this round synchronization algorithm to solve Byzantine SMR with the same asymptotic performance. The first part of the talk is based on joint work with Shir Cohen and Alexander Spiegelman, and the second part of the talk is based on joint work with Oded Naor.
Cite as

Idit Keidar. Byzantine Agreement and SMR with Sub-Quadratic Message Complexity (Invited Talk). In 24th International Conference on Principles of Distributed Systems (OPODIS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 184, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{keidar:LIPIcs.OPODIS.2020.2,
  author =	{Keidar, Idit},
  title =	{{Byzantine Agreement and SMR with Sub-Quadratic Message Complexity}},
  booktitle =	{24th International Conference on Principles of Distributed Systems (OPODIS 2020)},
  pages =	{2:1--2:1},
  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.2020.2},
  URN =		{urn:nbn:de:0030-drops-134874},
  doi =		{10.4230/LIPIcs.OPODIS.2020.2},
  annote =	{Keywords: Distributed Computing, Byzantine Agreement}
}
Document
DOI: 10.4230/LIPIcs.DISC.2020.26
Expected Linear Round Synchronization: The Missing Link for Linear Byzantine SMR

Authors: Oded Naor and Idit Keidar

Published in: LIPIcs, Volume 179, 34th International Symposium on Distributed Computing (DISC 2020)

Abstract
State Machine Replication (SMR) solutions often divide time into rounds, with a designated leader driving decisions in each round. Progress is guaranteed once all correct processes synchronize to the same round, and the leader of that round is correct. Recently suggested Byzantine SMR solutions such as HotStuff, Tendermint, and LibraBFT achieve progress with a linear message complexity and a constant time complexity once such round synchronization occurs. But round synchronization itself incurs an additional cost. By Dolev and Reischuk’s lower bound, any deterministic solution must have Ω(n²) communication complexity. Yet the question of randomized round synchronization with an expected linear message complexity remained open. We present an algorithm that, for the first time, achieves round synchronization with expected linear message complexity and expected constant latency. Existing protocols can use our round synchronization algorithm to solve Byzantine SMR with the same asymptotic performance.
Cite as

Oded Naor and Idit Keidar. Expected Linear Round Synchronization: The Missing Link for Linear Byzantine SMR. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 26:1-26:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{naor_et_al:LIPIcs.DISC.2020.26,
  author =	{Naor, Oded and Keidar, Idit},
  title =	{{Expected Linear Round Synchronization: The Missing Link for Linear Byzantine SMR}},
  booktitle =	{34th International Symposium on Distributed Computing (DISC 2020)},
  pages =	{26:1--26:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-168-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{179},
  editor =	{Attiya, Hagit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2020.26},
  URN =		{urn:nbn:de:0030-drops-131046},
  doi =		{10.4230/LIPIcs.DISC.2020.26},
  annote =	{Keywords: Distributed Systems, State Machine Replication}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2020.43
Nearly Optimal Embeddings of Flat Tori

Authors: Ishan Agarwal, Oded Regev, and Yi Tang

Published in: LIPIcs, Volume 176, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)

Abstract
We show that for any n-dimensional lattice ℒ ⊆ ℝⁿ, the torus ℝⁿ/ℒ can be embedded into Hilbert space with O(√{nlog n}) distortion. This improves the previously best known upper bound of O(n√{log n}) shown by Haviv and Regev (APPROX 2010, J. Topol. Anal. 2013) and approaches the lower bound of Ω(√n) due to Khot and Naor (FOCS 2005, Math. Ann. 2006).
Cite as

Ishan Agarwal, Oded Regev, and Yi Tang. Nearly Optimal Embeddings of Flat Tori. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 43:1-43:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{agarwal_et_al:LIPIcs.APPROX/RANDOM.2020.43,
  author =	{Agarwal, Ishan and Regev, Oded and Tang, Yi},
  title =	{{Nearly Optimal Embeddings of Flat Tori}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{43:1--43:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-164-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{176},
  editor =	{Byrka, Jaros{\l}aw and Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2020.43},
  URN =		{urn:nbn:de:0030-drops-126464},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.43},
  annote =	{Keywords: Lattices, metric embeddings, flat torus}
}
Document
DOI: 10.4230/LIPIcs.DISC.2019.30
Small Cuts and Connectivity Certificates: A Fault Tolerant Approach

Authors: Merav Parter

Published in: LIPIcs, Volume 146, 33rd International Symposium on Distributed Computing (DISC 2019)

Abstract
We revisit classical connectivity problems in the {CONGEST} model of distributed computing. By using techniques from fault tolerant network design, we show improved constructions, some of which are even "local" (i.e., with O~(1) rounds) for problems that are closely related to hard global problems (i.e., with a lower bound of Omega(Diam+sqrt{n}) rounds). Distributed Minimum Cut: Nanongkai and Su presented a randomized algorithm for computing a (1+epsilon)-approximation of the minimum cut using O~(D +sqrt{n}) rounds where D is the diameter of the graph. For a sufficiently large minimum cut lambda=Omega(sqrt{n}), this is tight due to Das Sarma et al. [FOCS '11], Ghaffari and Kuhn [DISC '13]. - Small Cuts: A special setting that remains open is where the graph connectivity lambda is small (i.e., constant). The only lower bound for this case is Omega(D), with a matching bound known only for lambda <= 2 due to Pritchard and Thurimella [TALG '11]. Recently, Daga, Henzinger, Nanongkai and Saranurak [STOC '19] raised the open problem of computing the minimum cut in poly(D) rounds for any lambda=O(1). In this paper, we resolve this problem by presenting a surprisingly simple algorithm, that takes a completely different approach than the existing algorithms. Our algorithm has also the benefit that it computes all minimum cuts in the graph, and naturally extends to vertex cuts as well. At the heart of the algorithm is a graph sampling approach usually used in the context of fault tolerant (FT) design. - Deterministic Algorithms: While the existing distributed minimum cut algorithms are randomized, our algorithm can be made deterministic within the same round complexity. To obtain this, we introduce a novel definition of universal sets along with their efficient computation. This allows us to derandomize the FT graph sampling technique, which might be of independent interest. - Computation of all Edge Connectivities: We also consider the more general task of computing the edge connectivity of all the edges in the graph. In the output format, it is required that the endpoints u,v of every edge (u,v) learn the cardinality of the u-v cut in the graph. We provide the first sublinear algorithm for this problem for the case of constant connectivity values. Specifically, by using the recent notion of low-congestion cycle cover, combined with the sampling technique, we compute all edge connectivities in poly(D) * 2^{O(sqrt{log n log log n})} rounds. Sparse Certificates: For an n-vertex graph G and an integer lambda, a lambda-sparse certificate H is a subgraph H subseteq G with O(lambda n) edges which is lambda-connected iff G is lambda-connected. For D-diameter graphs, constructions of sparse certificates for lambda in {2,3} have been provided by Thurimella [J. Alg. '97] and Dori [PODC '18] respectively using O~(D) number of rounds. The problem of devising such certificates with o(D+sqrt{n}) rounds was left open by Dori [PODC '18] for any lambda >= 4. Using connections to fault tolerant spanners, we considerably improve the round complexity for any lambda in [1,n] and epsilon in (0,1), by showing a construction of (1-epsilon)lambda-sparse certificates with O(lambda n) edges using only O(1/epsilon^2 * log^{2+o(1)} n) rounds.
Cite as

Merav Parter. Small Cuts and Connectivity Certificates: A Fault Tolerant Approach. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 30:1-30:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{parter:LIPIcs.DISC.2019.30,
  author =	{Parter, Merav},
  title =	{{Small Cuts and Connectivity Certificates: A Fault Tolerant Approach}},
  booktitle =	{33rd International Symposium on Distributed Computing (DISC 2019)},
  pages =	{30:1--30:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-126-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{146},
  editor =	{Suomela, Jukka},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.30},
  URN =		{urn:nbn:de:0030-drops-113371},
  doi =		{10.4230/LIPIcs.DISC.2019.30},
  annote =	{Keywords: Connectivity, Minimum Cut, Spanners}
}
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