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Documents authored by Gelles, Ran


Document
Beeping Shortest Paths via Hypergraph Bipartite Decomposition

Authors: Fabien Dufoulon, Yuval Emek, and Ran Gelles

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


Abstract
Constructing a shortest path between two network nodes is a fundamental task in distributed computing. This work develops schemes for the construction of shortest paths in randomized beeping networks between a predetermined source node and an arbitrary set of destination nodes. Our first scheme constructs a (single) shortest path to an arbitrary destination in O(D log log n + log³ n) rounds with high probability. Our second scheme constructs multiple shortest paths, one per each destination, in O(D log² n + log³ n) rounds with high probability. Our schemes are based on a reduction of the above shortest path construction tasks to a decomposition of hypergraphs into bipartite hypergraphs: We develop a beeping procedure that partitions the hyperedge set of a hypergraph H = (V_H, E_H) into k = Θ (log² n) disjoint subsets F₁ ∪ ⋯ ∪ F_k = E_H such that the (sub-)hypergraph (V_H, F_i) is bipartite in the sense that there exists a vertex subset U ⊆ V such that |U ∩ e| = 1 for every e ∈ F_i. This procedure turns out to be instrumental in speeding up shortest path constructions under the beeping model.

Cite as

Fabien Dufoulon, Yuval Emek, and Ran Gelles. Beeping Shortest Paths via Hypergraph Bipartite Decomposition. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 45:1-45:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{dufoulon_et_al:LIPIcs.ITCS.2023.45,
  author =	{Dufoulon, Fabien and Emek, Yuval and Gelles, Ran},
  title =	{{Beeping Shortest Paths via Hypergraph Bipartite Decomposition}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{45:1--45:24},
  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.2023.45},
  URN =		{urn:nbn:de:0030-drops-175485},
  doi =		{10.4230/LIPIcs.ITCS.2023.45},
  annote =	{Keywords: Beeping Networks, Shortest Paths, Hypergraph Bipartite Decomposition}
}
Document
Interactive Coding Resilient to an Unknown Number of Erasures

Authors: Ran Gelles and Siddharth Iyer

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


Abstract
We consider distributed computations between two parties carried out over a noisy channel that may erase messages. Following a noise model proposed by Dani et al. (2018), the noise level observed by the parties during the computation in our setting is arbitrary and a priori unknown to the parties. We develop interactive coding schemes that adapt to the actual level of noise and correctly execute any two-party computation. Namely, in case the channel erases T transmissions, the coding scheme will take N+2T transmissions using an alphabet of size 4 (alternatively, using 2N+4T transmissions over a binary channel) to correctly simulate any binary protocol that takes N transmissions assuming a noiseless channel. We can further reduce the communication to N+T by relaxing the communication model and allowing parties to remain silent rather than forcing them to communicate in every round of the coding scheme. Our coding schemes are efficient, deterministic, have linear overhead both in their communication and round complexity, and succeed (with probability 1) regardless of the number of erasures T.

Cite as

Ran Gelles and Siddharth Iyer. Interactive Coding Resilient to an Unknown Number of Erasures. In 23rd International Conference on Principles of Distributed Systems (OPODIS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 153, pp. 13:1-13:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{gelles_et_al:LIPIcs.OPODIS.2019.13,
  author =	{Gelles, Ran and Iyer, Siddharth},
  title =	{{Interactive Coding Resilient to an Unknown Number of Erasures}},
  booktitle =	{23rd International Conference on Principles of Distributed Systems (OPODIS 2019)},
  pages =	{13:1--13:16},
  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.2019.13},
  URN =		{urn:nbn:de:0030-drops-117999},
  doi =		{10.4230/LIPIcs.OPODIS.2019.13},
  annote =	{Keywords: Interactive coding, erasure channels, distributed computation with noise, unbounded noise}
}
Document
Optimal Short-Circuit Resilient Formulas

Authors: Mark Braverman, Klim Efremenko, Ran Gelles, and Michael A. Yitayew

Published in: LIPIcs, Volume 137, 34th Computational Complexity Conference (CCC 2019)


Abstract
We consider fault-tolerant boolean formulas in which the output of a faulty gate is short-circuited to one of the gate’s inputs. A recent result by Kalai et al. [FOCS 2012] converts any boolean formula into a resilient formula of polynomial size that works correctly if less than a fraction 1/6 of the gates (on every input-to-output path) are faulty. We improve the result of Kalai et al., and show how to efficiently fortify any boolean formula against a fraction 1/5 of short-circuit gates per path, with only a polynomial blowup in size. We additionally show that it is impossible to obtain formulas with higher resilience and sub-exponential growth in size. Towards our results, we consider interactive coding schemes when noiseless feedback is present; these produce resilient boolean formulas via a Karchmer-Wigderson relation. We develop a coding scheme that resists up to a fraction 1/5 of corrupted transmissions in each direction of the interactive channel. We further show that such a level of noise is maximal for coding schemes with sub-exponential blowup in communication. Our coding scheme takes a surprising inspiration from Blockchain technology.

Cite as

Mark Braverman, Klim Efremenko, Ran Gelles, and Michael A. Yitayew. Optimal Short-Circuit Resilient Formulas. In 34th Computational Complexity Conference (CCC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 137, pp. 10:1-10:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{braverman_et_al:LIPIcs.CCC.2019.10,
  author =	{Braverman, Mark and Efremenko, Klim and Gelles, Ran and Yitayew, Michael A.},
  title =	{{Optimal Short-Circuit Resilient Formulas}},
  booktitle =	{34th Computational Complexity Conference (CCC 2019)},
  pages =	{10:1--10:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-116-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{137},
  editor =	{Shpilka, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2019.10},
  URN =		{urn:nbn:de:0030-drops-108326},
  doi =		{10.4230/LIPIcs.CCC.2019.10},
  annote =	{Keywords: Circuit Complexity, Noise-Resilient Circuits, Interactive Coding, Coding Theory, Karchmer-Wigderson Games}
}
Document
Making Asynchronous Distributed Computations Robust to Channel Noise

Authors: Keren Censor-Hillel, Ran Gelles, and Bernhard Haeupler

Published in: LIPIcs, Volume 94, 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)


Abstract
We consider the problem of making distributed computations robust to noise, in particular to worst-case (adversarial) corruptions of messages. We give a general distributed interactive coding scheme which simulates any asynchronous distributed protocol while tolerating a maximal corruption level of \Theta(1/n)-fraction of all messages. Our noise tolerance is optimal and is obtained with only a moderate overhead in the number of messages. Our result is the first fully distributed interactive coding scheme in which the topology of the communication network is not known in advance. Prior work required either a coordinating node to be connected to all other nodes in the network or assumed a synchronous network in which all nodes already know the complete topology of the network. Overcoming this more realistic setting of an unknown topology leads to intriguing distributed problems, in which nodes try to learn sufficient information about the network topology in order to perform efficient coding and routing operations for coping with the noise. What makes these problems hard is that these topology exploration computations themselves must already be robust to noise.

Cite as

Keren Censor-Hillel, Ran Gelles, and Bernhard Haeupler. Making Asynchronous Distributed Computations Robust to Channel Noise. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 50:1-50:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{censorhillel_et_al:LIPIcs.ITCS.2018.50,
  author =	{Censor-Hillel, Keren and Gelles, Ran and Haeupler, Bernhard},
  title =	{{Making Asynchronous Distributed Computations Robust to Channel Noise}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{50:1--50:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-060-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{94},
  editor =	{Karlin, Anna R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2018.50},
  URN =		{urn:nbn:de:0030-drops-83184},
  doi =		{10.4230/LIPIcs.ITCS.2018.50},
  annote =	{Keywords: Distributed Computation, Coding for Interactive Communication, Noise- Resilient Computation, Coding Theory}
}
Document
Constant-Rate Interactive Coding Is Impossible, Even In Constant-Degree Networks

Authors: Ran Gelles and Yael T. Kalai

Published in: LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)


Abstract
Multiparty interactive coding allows a network of n parties to perform distributed computations when the communication channels suffer from noise. Previous results (Rajagopalan and Schulman, STOC’94) obtained a multiparty interactive coding protocol, resilient to random noise, with a blowup of O(log(\Delta + 1)) for networks whose topology has a maximal degree \Delta. Vitally, the communication model in their work forces all the parties to send one message at every round of the protocol, even if they have nothing to send. We re-examine the question of multiparty interactive coding, lifting the requirement that forces all the parties to communicate at each and every round. We use the recently developed information-theoretic machinery of Braverman et al. (STOC ’16) to show that if the network’s topology is a cycle, then there is a specific “cycle task” for which any coding scheme has a communication blowup of \Omega(log n). This is quite surprising since the cycle has a maximal degree of \Delta = 2, implying a coding with a constant blowup when all parties are forced to speak at all rounds. We complement our lower bound with a matching coding scheme for the "cycle task" that has a communication blowup of \Omega(log n). This makes our lower bound for the cycle task tight.

Cite as

Ran Gelles and Yael T. Kalai. Constant-Rate Interactive Coding Is Impossible, Even In Constant-Degree Networks. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 21:1-21:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{gelles_et_al:LIPIcs.ITCS.2017.21,
  author =	{Gelles, Ran and T. Kalai, Yael},
  title =	{{Constant-Rate Interactive Coding Is Impossible, Even In Constant-Degree Networks}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{21:1--21:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Papadimitriou, Christos H.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.21},
  URN =		{urn:nbn:de:0030-drops-81523},
  doi =		{10.4230/LIPIcs.ITCS.2017.21},
  annote =	{Keywords: Interactive Communication, Coding, Stochastic Noise, Communication Complexity}
}
Document
Coding for Interactive Communication Correcting Insertions and Deletions

Authors: Mark Braverman, Ran Gelles, Jieming Mao, and Rafail Ostrovsky

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)


Abstract
We consider the question of interactive communication, in which two remote parties perform a computation while their communication channel is (adversarially) noisy. We extend here the discussion into a more general and stronger class of noise, namely, we allow the channel to perform insertions and deletions of symbols. These types of errors may bring the parties "out of sync", so that there is no consensus regarding the current round of the protocol. In this more general noise model, we obtain the first interactive coding scheme that has a constant rate and tolerates noise rates of up to 1/18 - epsilon. To this end we develop a novel primitive we name edit distance tree code. The edit distance tree code is designed to replace the Hamming distance constraints in Schulman's tree codes (STOC 93), with a stronger edit distance requirement. However, the straightforward generalization of tree codes to edit distance does not seem to yield a primitive that suffices for communication in the presence of synchronization problems. Giving the "right" definition of edit distance tree codes is a main conceptual contribution of this work.

Cite as

Mark Braverman, Ran Gelles, Jieming Mao, and Rafail Ostrovsky. Coding for Interactive Communication Correcting Insertions and Deletions. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 61:1-61:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{braverman_et_al:LIPIcs.ICALP.2016.61,
  author =	{Braverman, Mark and Gelles, Ran and Mao, Jieming and Ostrovsky, Rafail},
  title =	{{Coding for Interactive Communication Correcting Insertions and Deletions}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{61:1--61:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.61},
  URN =		{urn:nbn:de:0030-drops-61981},
  doi =		{10.4230/LIPIcs.ICALP.2016.61},
  annote =	{Keywords: Interactive communication, coding, edit distance}
}
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