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**Published in:** LIPIcs, Volume 286, 27th International Conference on Principles of Distributed Systems (OPODIS 2023)

We consider the message complexity of verifying whether a given subgraph of the communication network forms a tree with specific properties both in the KT_ρ (nodes know their ρ-hop neighborhood, including node ids) and the KT₀ (nodes do not have this knowledge) models. We develop a rather general framework that helps in establishing tight lower bounds for various tree verification problems. We also consider two different verification requirements: namely that every node detects in the case the input is incorrect, as well as the requirement that at least one node detects. The results are stronger than previous ones in the sense that we assume that each node knows the number n of nodes in the graph (in some cases) or an α approximation of n (in other cases). For spanning tree verification, we show that the message complexity inherently depends on the quality of the given approximation of n: We show a tight lower bound of Ω(n²) for the case α ≥ √2 and a much better upper bound (i.e., O(n log n)) when nodes are given a tighter approximation. On the other hand, our framework also yields an Ω(n²) lower bound on the message complexity of verifying a minimum spanning tree (MST), which reveals a polynomial separation between ST verification and MST verification. This result holds for randomized algorithms with perfect knowledge of the network size, and even when just one node detects illegal inputs, thus improving over the work of Kor, Korman, and Peleg (2013). For verifying a d-approximate BFS tree, we show that the same lower bound holds even if nodes know n exactly, however, the lower bounds is sensitive to d, which is the stretch parameter. First, under the KT₀ assumption, we show a tight message complexity lower bound of Ω(n²) in the LOCAL model, when d ≤ n/(2+Ω(1)). For the KT_ρ assumption, we obtain an upper bound on the message complexity of O(nlog n) in the CONGEST model, when d ≥ (n-1)/max{2,ρ+1}, and use a novel charging argument to show that Ω((1/ρ)(n/ρ)^{1+c/ρ}) messages are required even in the LOCAL model for comparison-based algorithms. For the well-studied special case of KT₁, we obtain a tight lower bound of Ω(n²).

Shay Kutten, Peter Robinson, and Ming Ming Tan. Tight Bounds on the Message Complexity of Distributed Tree Verification. In 27th International Conference on Principles of Distributed Systems (OPODIS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 286, pp. 26:1-26:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kutten_et_al:LIPIcs.OPODIS.2023.26, author = {Kutten, Shay and Robinson, Peter and Tan, Ming Ming}, title = {{Tight Bounds on the Message Complexity of Distributed Tree Verification}}, booktitle = {27th International Conference on Principles of Distributed Systems (OPODIS 2023)}, pages = {26:1--26:22}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-308-9}, ISSN = {1868-8969}, year = {2024}, volume = {286}, editor = {Bessani, Alysson and D\'{e}fago, Xavier and Nakamura, Junya and Wada, Koichi and Yamauchi, Yukiko}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2023.26}, URN = {urn:nbn:de:0030-drops-195163}, doi = {10.4230/LIPIcs.OPODIS.2023.26}, annote = {Keywords: Distributed Graph Algorithm, Lower Bound} }

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

A singularly (near) optimal distributed algorithm is one that is (near) optimal in two criteria, namely, its time and message complexities. For synchronous CONGEST networks, such algorithms are known for fundamental distributed computing problems such as leader election [Kutten et al., JACM 2015] and Minimum Spanning Tree (MST) construction [Pandurangan et al., STOC 2017, Elkin, PODC 2017]. However, it is open whether a singularly (near) optimal bound can be obtained for the MST construction problem in general asynchronous CONGEST networks.
In this paper, we present a randomized distributed MST algorithm that, with high probability, computes an MST in asynchronous CONGEST networks and takes Õ(D^{1+ε} + √n) time and Õ(m) messages, where n is the number of nodes, m the number of edges, D is the diameter of the network, and ε > 0 is an arbitrarily small constant (both time and message bounds hold with high probability). Since Ω̃(D+√n) and Ω(m) are respective time and message lower bounds for distributed MST construction in the standard KT₀ model, our algorithm is message optimal (up to a polylog(n) factor) and almost time optimal (except for a D^ε factor). Our result answers an open question raised in Mashregi and King [DISC 2019] by giving the first known asynchronous MST algorithm that has sublinear time (for all D = O(n^{1-ε})) and uses Õ(m) messages. Using a result of Mashregi and King [DISC 2019], this also yields the first asynchronous MST algorithm that is sublinear in both time and messages in the KT₁ CONGEST model.
A key tool in our algorithm is the construction of a low diameter rooted spanning tree in asynchronous CONGEST that has depth Õ(D^{1+ε}) (for an arbitrarily small constant ε > 0) in Õ(D^{1+ε}) time and Õ(m) messages. To the best of our knowledge, this is the first such construction that is almost singularly optimal in the asynchronous setting. This tree construction may be of independent interest as it can also be used for efficiently performing basic tasks such as verified broadcast and convergecast in asynchronous networks.

Fabien Dufoulon, Shay Kutten, William K. Moses Jr., Gopal Pandurangan, and David Peleg. An Almost Singularly Optimal Asynchronous Distributed MST Algorithm. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 19:1-19:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dufoulon_et_al:LIPIcs.DISC.2022.19, author = {Dufoulon, Fabien and Kutten, Shay and Moses Jr., William K. and Pandurangan, Gopal and Peleg, David}, title = {{An Almost Singularly Optimal Asynchronous Distributed MST Algorithm}}, booktitle = {36th International Symposium on Distributed Computing (DISC 2022)}, pages = {19:1--19:24}, 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.2022.19}, URN = {urn:nbn:de:0030-drops-172107}, doi = {10.4230/LIPIcs.DISC.2022.19}, annote = {Keywords: Asynchronous networks, Minimum Spanning Tree, Distributed Algorithm, Singularly Optimal} }

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

Introduced by Korman, Kutten, and Peleg (PODC 2005), a proof labeling scheme (PLS) is a distributed verification system dedicated to evaluating if a given configured graph satisfies a certain property. It involves a centralized prover, whose role is to provide proof that a given configured graph is a yes-instance by means of assigning labels to the nodes, and a distributed verifier, whose role is to verify the validity of the given proof via local access to the assigned labels. In this paper, we introduce the notion of a locally restricted PLS in which the prover’s power is restricted to that of a LOCAL algorithm with a polylogarithmic number of rounds. To circumvent inherent impossibilities of PLSs in the locally restricted setting, we turn to models that relax the correctness requirements by allowing the verifier to accept some no-instances as long as they are not "too far" from satisfying the property in question. To this end, we evaluate (1) distributed graph optimization problems (OptDGPs) based on the notion of an approximate proof labeling scheme (APLS) (analogous to the type of relaxation used in sequential approximation algorithms); and (2) configured graph families (CGFs) based on the notion of a testing proof labeling schemes (TPLS) (analogous to the type of relaxation used in property testing algorithms). The main contribution of the paper comes in the form of two generic compilers, one for OptDGPs and one for CGFs: given a black-box access to an APLS (resp., PLS) for a large class of OptDGPs (resp., CGFs), the compiler produces a locally restricted APLS (resp., TPLS) for the same problem, while losing at most a (1 + ε) factor in the scheme’s relaxation guarantee. An appealing feature of the two compilers is that they only require a logarithmic additive label size overhead.

Yuval Emek, Yuval Gil, and Shay Kutten. Locally Restricted Proof Labeling Schemes. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 20:1-20:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{emek_et_al:LIPIcs.DISC.2022.20, author = {Emek, Yuval and Gil, Yuval and Kutten, Shay}, title = {{Locally Restricted Proof Labeling Schemes}}, booktitle = {36th International Symposium on Distributed Computing (DISC 2022)}, pages = {20:1--20:22}, 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.2022.20}, URN = {urn:nbn:de:0030-drops-172111}, doi = {10.4230/LIPIcs.DISC.2022.20}, annote = {Keywords: proof labeling schemes, generic compilers, SLOCAL algorithms} }

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

This paper concerns designing distributed algorithms that are singularly optimal, i.e., algorithms that are simultaneously time and message optimal, for the fundamental leader election problem in asynchronous networks.
Kutten et al. (JACM 2015) presented a singularly near optimal randomized leader election algorithm for general synchronous networks that ran in O(D) time and used O(m log n) messages (where D, m, and n are the network’s diameter, number of edges and number of nodes, respectively) with high probability. Both bounds are near optimal (up to a logarithmic factor), since Ω(D) and Ω(m) are the respective lower bounds for time and messages for leader election even for synchronous networks and even for (Monte-Carlo) randomized algorithms. On the other hand, for general asynchronous networks, leader election algorithms are only known that are either time or message optimal, but not both. Kutten et al. (DISC 2020) presented a randomized asynchronous leader election algorithm that is singularly near optimal for complete networks, but left open the problem for general networks.
This paper shows that singularly near optimal (up to polylogarithmic factors) bounds can be achieved for general asynchronous networks. We present a randomized singularly near optimal leader election algorithm that runs in O(D + log² n) time and O(m log² n) messages with high probability. Our result is the first known distributed leader election algorithm for asynchronous networks that is near optimal with respect to both time and message complexity and improves over a long line of results including the classical results of Gallager et al. (ACM TOPLAS, 1983), Peleg (JPDC, 1989), and Awerbuch (STOC, 89).

Shay Kutten, William K. Moses Jr., Gopal Pandurangan, and David Peleg. Singularly Near Optimal Leader Election in Asynchronous Networks. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 27:1-27:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{kutten_et_al:LIPIcs.DISC.2021.27, author = {Kutten, Shay and Moses Jr., William K. and Pandurangan, Gopal and Peleg, David}, title = {{Singularly Near Optimal Leader Election in Asynchronous Networks}}, booktitle = {35th International Symposium on Distributed Computing (DISC 2021)}, pages = {27:1--27:18}, 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.2021.27}, URN = {urn:nbn:de:0030-drops-148294}, doi = {10.4230/LIPIcs.DISC.2021.27}, annote = {Keywords: Leader election, Singular optimality, Randomized algorithms, Asynchronous networks, Arbitrary graphs} }

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**Published in:** LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

This paper considers a variant of the online paging problem, where the online algorithm has access to multiple predictors, each producing a sequence of predictions for the page arrival times. The predictors may have occasional prediction errors and it is assumed that at least one of them makes a sublinear number of prediction errors in total. Our main result states that this assumption suffices for the design of a randomized online algorithm whose time-average regret with respect to the optimal offline algorithm tends to zero as the time tends to infinity. This holds (with different regret bounds) for both the full information access model, where in each round, the online algorithm gets the predictions of all predictors, and the bandit access model, where in each round, the online algorithm queries a single predictor.
While online algorithms that exploit inaccurate predictions have been a topic of growing interest in the last few years, to the best of our knowledge, this is the first paper that studies this topic in the context of multiple predictors for an online problem with unbounded request sequences. Moreover, to the best of our knowledge, this is also the first paper that aims for (and achieves) online algorithms with a vanishing regret for a classic online problem under reasonable assumptions.

Yuval Emek, Shay Kutten, and Yangguang Shi. Online Paging with a Vanishing Regret. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 67:1-67:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{emek_et_al:LIPIcs.ITCS.2021.67, author = {Emek, Yuval and Kutten, Shay and Shi, Yangguang}, title = {{Online Paging with a Vanishing Regret}}, booktitle = {12th Innovations in Theoretical Computer Science Conference (ITCS 2021)}, pages = {67:1--67:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-177-1}, ISSN = {1868-8969}, year = {2021}, volume = {185}, editor = {Lee, James R.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.67}, URN = {urn:nbn:de:0030-drops-136065}, doi = {10.4230/LIPIcs.ITCS.2021.67}, annote = {Keywords: online paging, inaccurate predictions, multiple predictors, vanishing regret, full information vs. bandit access} }

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

This paper presents a randomized self-stabilizing algorithm that elects a leader r in a general n-node undirected graph and constructs a spanning tree T rooted at r. The algorithm works under the synchronous message passing network model, assuming that the nodes know a linear upper bound on n and that each edge has a unique ID known to both its endpoints (or, alternatively, assuming the KT₁ model). The highlight of this algorithm is its superior communication efficiency: It is guaranteed to send a total of Õ (n) messages, each of constant size, till stabilization, while stabilizing in Õ (n) rounds, in expectation and with high probability. After stabilization, the algorithm sends at most one constant size message per round while communicating only over the (n - 1) edges of T. In all these aspects, the communication overhead of the new algorithm is far smaller than that of the existing (mostly deterministic) self-stabilizing leader election algorithms.
The algorithm is relatively simple and relies mostly on known modules that are common in the fault free leader election literature; these modules are enhanced in various subtle ways in order to assemble them into a communication efficient self-stabilizing algorithm.

Xavier Défago, Yuval Emek, Shay Kutten, Toshimitsu Masuzawa, and Yasumasa Tamura. Communication Efficient Self-Stabilizing Leader Election. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 11:1-11:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{defago_et_al:LIPIcs.DISC.2020.11, author = {D\'{e}fago, Xavier and Emek, Yuval and Kutten, Shay and Masuzawa, Toshimitsu and Tamura, Yasumasa}, title = {{Communication Efficient Self-Stabilizing Leader Election}}, booktitle = {34th International Symposium on Distributed Computing (DISC 2020)}, pages = {11:1--11:19}, 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.2020.11}, URN = {urn:nbn:de:0030-drops-130892}, doi = {10.4230/LIPIcs.DISC.2020.11}, annote = {Keywords: self-stabilization, leader election, communication overhead} }

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

This paper concerns designing distributed algorithms that are singularly optimal, i.e., algorithms that are simultaneously time and message optimal, for the fundamental leader election problem in networks. Our main result is a randomized distributed leader election algorithm for asynchronous complete networks that is essentially (up to a polylogarithmic factor) singularly optimal. Our algorithm uses O(n) messages with high probability and runs in O(log² n) time (with high probability) to elect a unique leader. The O(n) message complexity should be contrasted with the Ω(n log n) lower bounds for the deterministic message complexity of leader election algorithms (regardless of time), proven by Korach, Moran, and Zaks (TCS, 1989) for asynchronous algorithms and by Afek and Gafni (SIAM J. Comput., 1991) for synchronous networks. Hence, our result also separates the message complexities of randomized and deterministic leader election. More importantly, our (randomized) time complexity of O(log² n) for obtaining the optimal O(n) message complexity is significantly smaller than the long-standing Θ̃(n) time complexity obtained by Afek and Gafni and by Singh (SIAM J. Comput., 1997) for message optimal (deterministic) election in asynchronous networks. Afek and Gafni also conjectured that Θ̃(n) time would be optimal for message-optimal asynchronous algorithms. Our result shows that randomized algorithms are significantly faster.
Turning to synchronous complete networks, Afek and Gafni showed an essentially singularly optimal deterministic algorithm with O(log n) time and O(n log n) messages. Ramanathan et al. (Distrib. Comput. 2007) used randomization to improve the message complexity, and showed a randomized algorithm with O(n) messages but still with O(log n) time (with failure probability O(1 / log^{Ω(1)}n)). Our second result shows that synchronous complete networks admit a tightly singularly optimal randomized algorithm, with O(1) time and O(n) messages (both bounds are optimal). Moreover, our algorithm’s time bound holds with certainty, and its message bound holds with high probability, i.e., 1-1/n^c for constant c.
Our results demonstrate that leader election can be solved in a simultaneously message and time-efficient manner in asynchronous complete networks using randomization. It is open whether this is possible in asynchronous general networks.

Shay Kutten, William K. Moses Jr., Gopal Pandurangan, and David Peleg. Singularly Optimal Randomized Leader Election. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 22:1-22:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{kutten_et_al:LIPIcs.DISC.2020.22, author = {Kutten, Shay and Moses Jr., William K. and Pandurangan, Gopal and Peleg, David}, title = {{Singularly Optimal Randomized Leader Election}}, booktitle = {34th International Symposium on Distributed Computing (DISC 2020)}, pages = {22:1--22:18}, 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.2020.22}, URN = {urn:nbn:de:0030-drops-131002}, doi = {10.4230/LIPIcs.DISC.2020.22}, annote = {Keywords: Leader election, Asynchronous systems, Randomized algorithms, Singularly optimal, Complete networks} }

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**Published in:** LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

In most online problems with delay, clairvoyance (i.e. knowing the future delay of a request upon its arrival) is required for polylogarithmic competitiveness. In this paper, we show that this is not the case for set cover with delay (SCD) - specifically, we present the first non-clairvoyant algorithm, which is O(log n log m)-competitive, where n is the number of elements and m is the number of sets. This matches the best known result for the classic online set cover (a special case of non-clairvoyant SCD). Moreover, clairvoyance does not allow for significant improvement - we present lower bounds of Ω(√{log n}) and Ω(√{log m}) for SCD which apply for the clairvoyant case.
In addition, the competitiveness of our algorithm does not depend on the number of requests. Such a guarantee on the size of the universe alone was not previously known even for the clairvoyant case - the only previously-known algorithm (due to Carrasco et al.) is clairvoyant, with competitiveness that grows with the number of requests.
For the special case of vertex cover with delay, we show a simpler, deterministic algorithm which is 3-competitive (and also non-clairvoyant).

Yossi Azar, Ashish Chiplunkar, Shay Kutten, and Noam Touitou. Set Cover with Delay - Clairvoyance Is Not Required. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 8:1-8:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{azar_et_al:LIPIcs.ESA.2020.8, author = {Azar, Yossi and Chiplunkar, Ashish and Kutten, Shay and Touitou, Noam}, title = {{Set Cover with Delay - Clairvoyance Is Not Required}}, booktitle = {28th Annual European Symposium on Algorithms (ESA 2020)}, pages = {8:1--8:21}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-162-7}, ISSN = {1868-8969}, year = {2020}, volume = {173}, editor = {Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.8}, URN = {urn:nbn:de:0030-drops-128749}, doi = {10.4230/LIPIcs.ESA.2020.8}, annote = {Keywords: Set Cover, Delay, Clairvoyant} }

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

A new spanner construction algorithm is presented, working under the LOCAL model with unique edge IDs. Given an n-node communication graph, a spanner with a constant stretch and O(n^{1 + epsilon}) edges (for an arbitrarily small constant epsilon > 0) is constructed in a constant number of rounds sending O(n^{1 + epsilon}) messages whp. Consequently, we conclude that every t-round LOCAL algorithm can be transformed into an O(t)-round LOCAL algorithm that sends O(t * n^{1 + epsilon}) messages whp. This improves upon all previous message-reduction schemes for LOCAL algorithms that incur a log^{Omega (1)} n blow-up of the round complexity.

Shimon Bitton, Yuval Emek, Taisuke Izumi, and Shay Kutten. Message Reduction in the LOCAL Model Is a Free Lunch. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bitton_et_al:LIPIcs.DISC.2019.7, author = {Bitton, Shimon and Emek, Yuval and Izumi, Taisuke and Kutten, Shay}, title = {{Message Reduction in the LOCAL Model Is a Free Lunch}}, booktitle = {33rd International Symposium on Distributed Computing (DISC 2019)}, pages = {7:1--7:15}, 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.2019.7}, URN = {urn:nbn:de:0030-drops-113145}, doi = {10.4230/LIPIcs.DISC.2019.7}, annote = {Keywords: distributed graph algorithms, spanner, LOCAL model, message complexity} }

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**Published in:** LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

We study network coordination problems, as captured by the setting of generalized network design (Emek et al., STOC 2018), in the face of uncertainty resulting from partial information that the network users hold regarding the actions of their peers. This uncertainty is formalized using Alon et al.’s Bayesian ignorance framework (TCS 2012). While the approach of Alon et al. is purely combinatorial, the current paper takes into account computational considerations: Our main technical contribution is the development of (strongly) polynomial time algorithms for local decision making in the face of Bayesian uncertainty.

Yuval Emek, Shay Kutten, Ron Lavi, and Yangguang Shi. Bayesian Generalized Network Design. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 45:1-45:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{emek_et_al:LIPIcs.ESA.2019.45, author = {Emek, Yuval and Kutten, Shay and Lavi, Ron and Shi, Yangguang}, title = {{Bayesian Generalized Network Design}}, booktitle = {27th Annual European Symposium on Algorithms (ESA 2019)}, pages = {45:1--45:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-124-5}, ISSN = {1868-8969}, year = {2019}, volume = {144}, editor = {Bender, Michael A. and Svensson, Ola and Herman, Grzegorz}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.45}, URN = {urn:nbn:de:0030-drops-111660}, doi = {10.4230/LIPIcs.ESA.2019.45}, annote = {Keywords: approximation algorithms, Bayesian competitive ratio, Bayesian ignorance, generalized network design, diseconomies of scale, energy consumption, smoothness, best response dynamics} }

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Track C: Foundations of Networks and Multi-Agent Systems: Models, Algorithms and Information Management

**Published in:** LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Addressing a fundamental problem in programmable matter, we present the first deterministic algorithm to elect a unique leader in a system of connected amoebots assuming only that amoebots are initially contracted. Previous algorithms either used randomization, made various assumptions (shapes with no holes, or known shared chirality), or elected several co-leaders in some cases.
Some of the building blocks we introduce in constructing the algorithm are of interest by themselves, especially the procedure we present for reaching common chirality among the amoebots. Given the leader election and the chirality agreement building block, it is known that various tasks in programmable matter can be performed or improved.
The main idea of the new algorithm is the usage of the ability of the amoebots to move, which previous leader election algorithms have not used.

Yuval Emek, Shay Kutten, Ron Lavi, and William K. Moses Jr.. Deterministic Leader Election in Programmable Matter. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 140:1-140:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{emek_et_al:LIPIcs.ICALP.2019.140, author = {Emek, Yuval and Kutten, Shay and Lavi, Ron and Moses Jr., William K.}, title = {{Deterministic Leader Election in Programmable Matter}}, booktitle = {46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)}, pages = {140:1--140:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-109-2}, ISSN = {1868-8969}, year = {2019}, volume = {132}, editor = {Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.140}, URN = {urn:nbn:de:0030-drops-107169}, doi = {10.4230/LIPIcs.ICALP.2019.140}, annote = {Keywords: programmable matter, geometric amoebot model, leader election} }

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