16 Search Results for "Kol, Gillat"


Document
Track A: Algorithms, Complexity and Games
Protecting Single-Hop Radio Networks from Message Drops

Authors: Klim Efremenko, Gillat Kol, Dmitry Paramonov, and Raghuvansh R. Saxena

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)


Abstract
Single-hop radio networks (SHRN) are a well studied abstraction of communication over a wireless channel. In this model, in every round, each of the n participating parties may decide to broadcast a message to all the others, potentially causing collisions. We consider the SHRN model in the presence of stochastic message drops (i.e., erasures), where in every round, the message received by each party is erased (replaced by ⊥) with some small constant probability, independently. Our main result is a constant rate coding scheme, allowing one to run protocols designed to work over the (noiseless) SHRN model over the SHRN model with erasures. Our scheme converts any protocol Π of length at most exponential in n over the SHRN model to a protocol Π' that is resilient to constant fraction of erasures and has length linear in the length of Π. We mention that for the special case where the protocol Π is non-adaptive, i.e., the order of communication is fixed in advance, such a scheme was known. Nevertheless, adaptivity is widely used and is known to hugely boost the power of wireless channels, which makes handling the general case of adaptive protocols Π both important and more challenging. Indeed, to the best of our knowledge, our result is the first constant rate scheme that converts adaptive protocols to noise resilient ones in any multi-party model.

Cite as

Klim Efremenko, Gillat Kol, Dmitry Paramonov, and Raghuvansh R. Saxena. Protecting Single-Hop Radio Networks from Message Drops. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 53:1-53:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{efremenko_et_al:LIPIcs.ICALP.2023.53,
  author =	{Efremenko, Klim and Kol, Gillat and Paramonov, Dmitry and Saxena, Raghuvansh R.},
  title =	{{Protecting Single-Hop Radio Networks from Message Drops}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{53:1--53:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.53},
  URN =		{urn:nbn:de:0030-drops-181059},
  doi =		{10.4230/LIPIcs.ICALP.2023.53},
  annote =	{Keywords: Radio Networks, Interactive Coding, Error Correcting Codes}
}
Document
Noisy Radio Network Lower Bounds via Noiseless Beeping Lower Bounds

Authors: Klim Efremenko, Gillat Kol, Dmitry Paramonov, and Raghuvansh R. Saxena

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


Abstract
Much of today’s communication is carried out over large wireless systems with different input-output behaviors. In this work, we compare the power of central abstractions of wireless communication through the general notion of boolean symmetric f-channels: In every round of the f-channel, each of its n parties decides to either broadcast or not, and the channel outputs f(m), where m is the number of broadcasting parties. Our first result is that the well studied beeping channel, where f is the threshold-1 function, is not stronger than any other f-channel. To this end, we design a protocol over the f-channel and prove that any protocol that simulates it over the beeping channel blows up the round complexity by a factor of Ω(log n). Our lower bound technique may be of independent interest, as it essentially generalizes the popular fooling set technique by exploiting a "local" relaxation of combinatorial rectangles. Curiously, while this result shows the limitations of a noiseless channel, namely, the beeping channel, we are able to use it to show the limitations of the noisy version of many other channels. This includes the extensively studied single-hop radio network model with collisions-as-silence (CAS), which is equivalent to the f-channel with f(m) = 1 iff m = 1. In particular, our second and main result, obtained from the first, shows that converting CAS protocols to noise resilient ones may incur a large performance overhead, i.e., no constant rate interactive code exists. To this end, we design a CAS protocol and prove that any protocol that simulates it over the noisy CAS model with correlated stochastic noise, blows up the round complexity by a factor of Ω(log n). We mention that the Ω(log n) overhead in both our results is tight.

Cite as

Klim Efremenko, Gillat Kol, Dmitry Paramonov, and Raghuvansh R. Saxena. Noisy Radio Network Lower Bounds via Noiseless Beeping Lower Bounds. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 46:1-46:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{efremenko_et_al:LIPIcs.ITCS.2023.46,
  author =	{Efremenko, Klim and Kol, Gillat and Paramonov, Dmitry and Saxena, Raghuvansh R.},
  title =	{{Noisy Radio Network Lower Bounds via Noiseless Beeping Lower Bounds}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{46:1--46:20},
  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.2023.46},
  URN =		{urn:nbn:de:0030-drops-175499},
  doi =		{10.4230/LIPIcs.ITCS.2023.46},
  annote =	{Keywords: Beeping Model, Radio Networks}
}
Document
Characterizing the Multi-Pass Streaming Complexity for Solving Boolean CSPs Exactly

Authors: Gillat Kol, Dmitry Paramonov, Raghuvansh R. Saxena, and Huacheng Yu

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


Abstract
We study boolean constraint satisfaction problems (CSPs) Max-CSP^f_n for all predicates f: {0,1}^k → {0,1}. In these problems, given an integer v and a list of constraints over n boolean variables, each obtained by applying f to a sequence of literals, we wish to decide if there is an assignment to the variables that satisfies at least v constraints. We consider these problems in the streaming model, where the algorithm makes a small number of passes over the list of constraints. Our first and main result is the following complete characterization: For every predicate f, the streaming space complexity of the Max-CSP^f_n problem is Θ̃(n^deg(f)), where deg(f) is the degree of f when viewed as a multilinear polynomial. While the upper bound is obtained by a (very simple) one-pass streaming algorithm, our lower bound shows that a better space complexity is impossible even with constant-pass streaming algorithms. Building on our techniques, we are also able to get an optimal Ω(n²) lower bound on the space complexity of constant-pass streaming algorithms for the well studied Max-CUT problem, even though it is not technically a Max-CSP^f_n problem as, e.g., negations of variables and repeated constraints are not allowed.

Cite as

Gillat Kol, Dmitry Paramonov, Raghuvansh R. Saxena, and Huacheng Yu. Characterizing the Multi-Pass Streaming Complexity for Solving Boolean CSPs Exactly. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 80:1-80:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{kol_et_al:LIPIcs.ITCS.2023.80,
  author =	{Kol, Gillat and Paramonov, Dmitry and Saxena, Raghuvansh R. and Yu, Huacheng},
  title =	{{Characterizing the Multi-Pass Streaming Complexity for Solving Boolean CSPs Exactly}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{80:1--80:15},
  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.2023.80},
  URN =		{urn:nbn:de:0030-drops-175837},
  doi =		{10.4230/LIPIcs.ITCS.2023.80},
  annote =	{Keywords: Streaming algorithms, Constraint Satisfaction Problems}
}
Document
Track A: Algorithms, Complexity and Games
Near-Optimal Two-Pass Streaming Algorithm for Sampling Random Walks over Directed Graphs

Authors: Lijie Chen, Gillat Kol, Dmitry Paramonov, Raghuvansh R. Saxena, Zhao Song, and Huacheng Yu

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)


Abstract
For a directed graph G with n vertices and a start vertex u_start, we wish to (approximately) sample an L-step random walk over G starting from u_start with minimum space using an algorithm that only makes few passes over the edges of the graph. This problem found many applications, for instance, in approximating the PageRank of a webpage. If only a single pass is allowed, the space complexity of this problem was shown to be Θ̃(n ⋅ L). Prior to our work, a better space complexity was only known with Õ(√L) passes. We essentially settle the space complexity of this random walk simulation problem for two-pass streaming algorithms, showing that it is Θ̃(n ⋅ √L), by giving almost matching upper and lower bounds. Our lower bound argument extends to every constant number of passes p, and shows that any p-pass algorithm for this problem uses Ω̃(n ⋅ L^{1/p}) space. In addition, we show a similar Θ̃(n ⋅ √L) bound on the space complexity of any algorithm (with any number of passes) for the related problem of sampling an L-step random walk from every vertex in the graph.

Cite as

Lijie Chen, Gillat Kol, Dmitry Paramonov, Raghuvansh R. Saxena, Zhao Song, and Huacheng Yu. Near-Optimal Two-Pass Streaming Algorithm for Sampling Random Walks over Directed Graphs. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 52:1-52:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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@InProceedings{chen_et_al:LIPIcs.ICALP.2021.52,
  author =	{Chen, Lijie and Kol, Gillat and Paramonov, Dmitry and Saxena, Raghuvansh R. and Song, Zhao and Yu, Huacheng},
  title =	{{Near-Optimal Two-Pass Streaming Algorithm for Sampling Random Walks over Directed Graphs}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{52:1--52:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.52},
  URN =		{urn:nbn:de:0030-drops-141218},
  doi =		{10.4230/LIPIcs.ICALP.2021.52},
  annote =	{Keywords: streaming algorithms, random walk sampling}
}
Document
Computation over the Noisy Broadcast Channel with Malicious Parties

Authors: Klim Efremenko, Gillat Kol, Dmitry Paramonov, and Raghuvansh R. Saxena

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


Abstract
We study the n-party noisy broadcast channel with a constant fraction of malicious parties. Specifically, we assume that each non-malicious party holds an input bit, and communicates with the others in order to learn the input bits of all non-malicious parties. In each communication round, one of the parties broadcasts a bit to all other parties, and the bit received by each party is flipped with a fixed constant probability (independently for each recipient). How many rounds are needed? Assuming there are no malicious parties, Gallager gave an 𝒪(n log log n)-round protocol for the above problem, which was later shown to be optimal. This protocol, however, inherently breaks down in the presence of malicious parties. We present a novel n ⋅ 𝒪̃(√{log n})-round protocol, that solves this problem even when almost half of the parties are malicious. Our protocol uses a new type of error correcting code, which we call a locality sensitive code and which may be of independent interest. Roughly speaking, these codes map "close" messages to "close" codewords, while messages that are not close are mapped to codewords that are very far apart. We view our result as a first step towards a theory of property preserving interactive coding, i.e., interactive codes that preserve useful properties of the protocol being encoded. In our case, the naive protocol over the noiseless broadcast channel, where all the parties broadcast their input bit and output all the bits received, works even in the presence of malicious parties. Our simulation of this protocol, unlike Gallager’s, preserves this property of the original protocol.

Cite as

Klim Efremenko, Gillat Kol, Dmitry Paramonov, and Raghuvansh R. Saxena. Computation over the Noisy Broadcast Channel with Malicious Parties. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 82:1-82:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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@InProceedings{efremenko_et_al:LIPIcs.ITCS.2021.82,
  author =	{Efremenko, Klim and Kol, Gillat and Paramonov, Dmitry and Saxena, Raghuvansh R.},
  title =	{{Computation over the Noisy Broadcast Channel with Malicious Parties}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{82:1--82:19},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.82},
  URN =		{urn:nbn:de:0030-drops-136215},
  doi =		{10.4230/LIPIcs.ITCS.2021.82},
  annote =	{Keywords: Broadcast Network, Malicious Parties, Communication Complexity}
}
Document
On the Computational Power of Radio Channels

Authors: Mark Braverman, Gillat Kol, Rotem Oshman, and Avishay Tal

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


Abstract
Radio networks can be a challenging platform for which to develop distributed algorithms, because the network nodes must contend for a shared channel. In some cases, though, the shared medium is an advantage rather than a disadvantage: for example, many radio network algorithms cleverly use the shared channel to approximate the degree of a node, or estimate the contention. In this paper we ask how far the inherent power of a shared radio channel goes, and whether it can efficiently compute "classicaly hard" functions such as Majority, Approximate Sum, and Parity. Using techniques from circuit complexity, we show that in many cases, the answer is "no". We show that simple radio channels, such as the beeping model or the channel with collision-detection, can be approximated by a low-degree polynomial, which makes them subject to known lower bounds on functions such as Parity and Majority; we obtain round lower bounds of the form Omega(n^{delta}) on these functions, for delta in (0,1). Next, we use the technique of random restrictions, used to prove AC^0 lower bounds, to prove a tight lower bound of Omega(1/epsilon^2) on computing a (1 +/- epsilon)-approximation to the sum of the nodes' inputs. Our techniques are general, and apply to many types of radio channels studied in the literature.

Cite as

Mark Braverman, Gillat Kol, Rotem Oshman, and Avishay Tal. On the Computational Power of Radio Channels. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 8:1-8:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)


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@InProceedings{braverman_et_al:LIPIcs.DISC.2019.8,
  author =	{Braverman, Mark and Kol, Gillat and Oshman, Rotem and Tal, Avishay},
  title =	{{On the Computational Power of Radio Channels}},
  booktitle =	{33rd International Symposium on Distributed Computing (DISC 2019)},
  pages =	{8:1--8:17},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.8},
  URN =		{urn:nbn:de:0030-drops-113152},
  doi =		{10.4230/LIPIcs.DISC.2019.8},
  annote =	{Keywords: radio channel, lower bounds, approximate majority}
}
Document
Optimal Separation and Strong Direct Sum for Randomized Query Complexity

Authors: Eric Blais and Joshua Brody

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


Abstract
We establish two results regarding the query complexity of bounded-error randomized algorithms. Bounded-error separation theorem. There exists a total function f : {0,1}^n -> {0,1} whose epsilon-error randomized query complexity satisfies overline{R}_epsilon(f) = Omega(R(f) * log 1/epsilon). Strong direct sum theorem. For every function f and every k >= 2, the randomized query complexity of computing k instances of f simultaneously satisfies overline{R}_epsilon(f^k) = Theta(k * overline{R}_{epsilon/k}(f)). As a consequence of our two main results, we obtain an optimal superlinear direct-sum-type theorem for randomized query complexity: there exists a function f for which R(f^k) = Theta(k log k * R(f)). This answers an open question of Drucker (2012). Combining this result with the query-to-communication complexity lifting theorem of Göös, Pitassi, and Watson (2017), this also shows that there is a total function whose public-coin randomized communication complexity satisfies R^{cc}(f^k) = Theta(k log k * R^{cc}(f)), answering a question of Feder, Kushilevitz, Naor, and Nisan (1995).

Cite as

Eric Blais and Joshua Brody. Optimal Separation and Strong Direct Sum for Randomized Query Complexity. In 34th Computational Complexity Conference (CCC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 137, pp. 29:1-29:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{blais_et_al:LIPIcs.CCC.2019.29,
  author =	{Blais, Eric and Brody, Joshua},
  title =	{{Optimal Separation and Strong Direct Sum for Randomized Query Complexity}},
  booktitle =	{34th Computational Complexity Conference (CCC 2019)},
  pages =	{29:1--29:17},
  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.2019.29},
  URN =		{urn:nbn:de:0030-drops-108511},
  doi =		{10.4230/LIPIcs.CCC.2019.29},
  annote =	{Keywords: Decision trees, query complexity, communication complexity}
}
Document
Time-Space Lower Bounds for Two-Pass Learning

Authors: Sumegha Garg, Ran Raz, and Avishay Tal

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


Abstract
A line of recent works showed that for a large class of learning problems, any learning algorithm requires either super-linear memory size or a super-polynomial number of samples [Raz, 2016; Kol et al., 2017; Raz, 2017; Moshkovitz and Moshkovitz, 2018; Beame et al., 2018; Garg et al., 2018]. For example, any algorithm for learning parities of size n requires either a memory of size Omega(n^{2}) or an exponential number of samples [Raz, 2016]. All these works modeled the learner as a one-pass branching program, allowing only one pass over the stream of samples. In this work, we prove the first memory-samples lower bounds (with a super-linear lower bound on the memory size and super-polynomial lower bound on the number of samples) when the learner is allowed two passes over the stream of samples. For example, we prove that any two-pass algorithm for learning parities of size n requires either a memory of size Omega(n^{1.5}) or at least 2^{Omega(sqrt{n})} samples. More generally, a matrix M: A x X - > {-1,1} corresponds to the following learning problem: An unknown element x in X is chosen uniformly at random. A learner tries to learn x from a stream of samples, (a_1, b_1), (a_2, b_2) ..., where for every i, a_i in A is chosen uniformly at random and b_i = M(a_i,x). Assume that k,l, r are such that any submatrix of M of at least 2^{-k} * |A| rows and at least 2^{-l} * |X| columns, has a bias of at most 2^{-r}. We show that any two-pass learning algorithm for the learning problem corresponding to M requires either a memory of size at least Omega (k * min{k,sqrt{l}}), or at least 2^{Omega(min{k,sqrt{l},r})} samples.

Cite as

Sumegha Garg, Ran Raz, and Avishay Tal. Time-Space Lower Bounds for Two-Pass Learning. In 34th Computational Complexity Conference (CCC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 137, pp. 22:1-22:39, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{garg_et_al:LIPIcs.CCC.2019.22,
  author =	{Garg, Sumegha and Raz, Ran and Tal, Avishay},
  title =	{{Time-Space Lower Bounds for Two-Pass Learning}},
  booktitle =	{34th Computational Complexity Conference (CCC 2019)},
  pages =	{22:1--22:39},
  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.2019.22},
  URN =		{urn:nbn:de:0030-drops-108446},
  doi =		{10.4230/LIPIcs.CCC.2019.22},
  annote =	{Keywords: branching program, time-space tradeoffs, two-pass streaming, PAC learning, lower bounds}
}
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
A Candidate for a Strong Separation of Information and Communication

Authors: Mark Braverman, Anat Ganor, Gillat Kol, and Ran Raz

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


Abstract
The weak interactive compression conjecture asserts that any two-party communication protocol with communication complexity C and information complexity I can be compressed to a protocol with communication complexity poly(I)polylog(C). We describe a communication problem that is a candidate for refuting that conjecture. Specifically, while we show that the problem can be solved by a protocol with communication complexity C and information complexity I=polylog(C), the problem seems to be hard for protocols with communication complexity poly(I)polylog(C)=polylog(C).

Cite as

Mark Braverman, Anat Ganor, Gillat Kol, and Ran Raz. A Candidate for a Strong Separation of Information and Communication. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 11:1-11:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


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@InProceedings{braverman_et_al:LIPIcs.ITCS.2018.11,
  author =	{Braverman, Mark and Ganor, Anat and Kol, Gillat and Raz, Ran},
  title =	{{A Candidate for a Strong Separation of Information and Communication}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{11:1--11:13},
  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.2018.11},
  URN =		{urn:nbn:de:0030-drops-83322},
  doi =		{10.4230/LIPIcs.ITCS.2018.11},
  annote =	{Keywords: communication complexity, amortized communication complexity, communication compression, direct sum, information complexity}
}
Document
Interactive Compression for Multi-Party Protocol

Authors: Gillat Kol, Rotem Oshman, and Dafna Sadeh

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


Abstract
The field of compression studies the question of how many bits of communication are necessary to convey a given piece of data. For one-way communication between a sender and a receiver, the seminal work of Shannon and Huffman showed that the communication required is characterized by the entropy of the data; in recent years, there has been a great amount of interest in extending this line of research to interactive communication, where instead of a sender and a receiver we have two parties communication back-and-forth. In this paper we initiate the study of interactive compression for distributed multi-player protocols. We consider the classical shared blackboard model, where players take turns speaking, and each player's message is immediately seen by all the other players. We show that in the shared blackboard model with k players, one can compress protocols down to ~O(Ik), where I is the information content of the protocol and k is the number of players. We complement this result with an almost matching lower bound of ~Omega(Ik), which shows that a nearly-linear dependence on the number of players cannot be avoided.

Cite as

Gillat Kol, Rotem Oshman, and Dafna Sadeh. Interactive Compression for Multi-Party Protocol. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 31:1-31:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)


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@InProceedings{kol_et_al:LIPIcs.DISC.2017.31,
  author =	{Kol, Gillat and Oshman, Rotem and Sadeh, Dafna},
  title =	{{Interactive Compression for Multi-Party Protocol}},
  booktitle =	{31st International Symposium on Distributed Computing (DISC 2017)},
  pages =	{31:1--31:15},
  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.2017.31},
  URN =		{urn:nbn:de:0030-drops-80111},
  doi =		{10.4230/LIPIcs.DISC.2017.31},
  annote =	{Keywords: interactive compression, multi-party communication}
}
Document
Internal Compression of Protocols to Entropy

Authors: Balthazar Bauer, Shay Moran, and Amir Yehudayoff

Published in: LIPIcs, Volume 40, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)


Abstract
We study internal compression of communication protocols to their internal entropy, which is the entropy of the transcript from the players' perspective. We provide two internal compression schemes with error. One of a protocol of Feige et al. for finding the first difference between two strings. The second and main one is an internal compression with error epsilon > 0 of a protocol with internal entropy H^{int} and communication complexity C to a protocol with communication at most order (H^{int}/epsilon)^2 * log(log(C)). This immediately implies a similar compression to the internal information of public-coin protocols, which provides an exponential improvement over previously known public-coin compressions in the dependence on C. It further shows that in a recent protocol of Ganor, Kol and Raz, it is impossible to move the private randomness to be public without an exponential cost. To the best of our knowledge, No such example was previously known.

Cite as

Balthazar Bauer, Shay Moran, and Amir Yehudayoff. Internal Compression of Protocols to Entropy. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 40, pp. 481-496, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{bauer_et_al:LIPIcs.APPROX-RANDOM.2015.481,
  author =	{Bauer, Balthazar and Moran, Shay and Yehudayoff, Amir},
  title =	{{Internal Compression of Protocols to Entropy}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
  pages =	{481--496},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-89-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{40},
  editor =	{Garg, Naveen and Jansen, Klaus and Rao, Anup and Rolim, Jos\'{e} D. P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2015.481},
  URN =		{urn:nbn:de:0030-drops-53198},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2015.481},
  annote =	{Keywords: Communication complexity, Information complexity, Compression, Simulation, Entropy}
}
Document
Communication with Partial Noiseless Feedback

Authors: Bernhard Haeupler, Pritish Kamath, and Ameya Velingker

Published in: LIPIcs, Volume 40, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)


Abstract
We introduce the notion of one-way communication schemes with partial noiseless feedback. In this setting, Alice wishes to communicate a message to Bob by using a communication scheme that involves sending a sequence of bits over a channel while receiving feedback bits from Bob for delta fraction of the transmissions. An adversary is allowed to corrupt up to a constant fraction of Alice's transmissions, while the feedback is always uncorrupted. Motivated by questions related to coding for interactive communication, we seek to determine the maximum error rate, as a function of 0 <= delta <= 1, such that Alice can send a message to Bob via some protocol with delta fraction of noiseless feedback. The case delta = 1 corresponds to full feedback, in which the result of Berlekamp ['64] implies that the maximum tolerable error rate is 1/3, while the case delta = 0 corresponds to no feedback, in which the maximum tolerable error rate is 1/4, achievable by use of a binary error-correcting code. In this work, we show that for any delta in (0,1] and gamma in [0, 1/3), there exists a randomized communication scheme with noiseless delta-feedback, such that the probability of miscommunication is low, as long as no more than a gamma fraction of the rounds are corrupted. Moreover, we show that for any delta in (0, 1] and gamma < f(delta), there exists a deterministic communication scheme with noiseless delta-feedback that always decodes correctly as long as no more than a gamma fraction of rounds are corrupted. Here f is a monotonically increasing, piecewise linear, continuous function with f(0) = 1/4 and f(1) = 1/3. Also, the rate of communication in both cases is constant (dependent on delta and gamma but independent of the input length).

Cite as

Bernhard Haeupler, Pritish Kamath, and Ameya Velingker. Communication with Partial Noiseless Feedback. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 40, pp. 881-897, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{haeupler_et_al:LIPIcs.APPROX-RANDOM.2015.881,
  author =	{Haeupler, Bernhard and Kamath, Pritish and Velingker, Ameya},
  title =	{{Communication with Partial Noiseless Feedback}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
  pages =	{881--897},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-89-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{40},
  editor =	{Garg, Naveen and Jansen, Klaus and Rao, Anup and Rolim, Jos\'{e} D. P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2015.881},
  URN =		{urn:nbn:de:0030-drops-53426},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2015.881},
  annote =	{Keywords: Communication with feedback, Interactive communication, Coding theory Digital}
}
Document
A Characterization of Hard-to-cover CSPs

Authors: Amey Bhangale, Prahladh Harsha, and Girish Varma

Published in: LIPIcs, Volume 33, 30th Conference on Computational Complexity (CCC 2015)


Abstract
We continue the study of covering complexity of constraint satisfaction problems (CSPs) initiated by Guruswami, Håstad and Sudan [SIAM J. Computing, 31(6):1663--1686, 2002] and Dinur and Kol [in Proc. 28th IEEE Conference on Computational Complexity, 2013]. The covering number of a CSP instance Phi, denoted by nu(Phi) is the smallest number of assignments to the variables of Phi, such that each constraint of Phi is satisfied by at least one of the assignments. We show the following results regarding how well efficient algorithms can approximate the covering number of a given CSP instance. 1. Assuming a covering unique games conjecture, introduced by Dinur and Kol, we show that for every non-odd predicate P over any constant sized alphabet and every integer K, it is NP-hard to distinguish between P-CSP instances (i.e., CSP instances where all the constraints are of type P) which are coverable by a constant number of assignments and those whose covering number is at least K. Previously, Dinur and Kol, using the same covering unique games conjecture, had shown a similar hardness result for every non-odd predicate over the Boolean alphabet that supports a pairwise independent distribution. Our generalization yields a complete characterization of CSPs over constant sized alphabet Sigma that are hard to cover since CSPs over odd predicates are trivially coverable with |Sigma| assignments. 2. For a large class of predicates that are contained in the 2k-LIN predicate, we show that it is quasi-NP-hard to distinguish between instances which have covering number at most two and covering number at least Omega(log(log(n))). This generalizes the 4-LIN result of Dinur and Kol that states it is quasi-NP-hard to distinguish between 4-LIN-CSP instances which have covering number at most two and covering number at least Omega(log(log(log(n)))).

Cite as

Amey Bhangale, Prahladh Harsha, and Girish Varma. A Characterization of Hard-to-cover CSPs. In 30th Conference on Computational Complexity (CCC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 33, pp. 280-303, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{bhangale_et_al:LIPIcs.CCC.2015.280,
  author =	{Bhangale, Amey and Harsha, Prahladh and Varma, Girish},
  title =	{{A Characterization of Hard-to-cover CSPs}},
  booktitle =	{30th Conference on Computational Complexity (CCC 2015)},
  pages =	{280--303},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-81-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{33},
  editor =	{Zuckerman, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2015.280},
  URN =		{urn:nbn:de:0030-drops-50574},
  doi =		{10.4230/LIPIcs.CCC.2015.280},
  annote =	{Keywords: CSPs, Covering Problem, Hardness of Approximation, Unique Games, Invariance Principle}
}
Document
How to Compress Asymmetric Communication

Authors: Sivaramakrishnan Natarajan Ramamoorthy and Anup Rao

Published in: LIPIcs, Volume 33, 30th Conference on Computational Complexity (CCC 2015)


Abstract
We study the relationship between communication and information in 2-party communication protocols when the information is asymmetric. If I^A denotes the number of bits of information revealed by the first party, I^B denotes the information revealed by the second party, and C is the number of bits of communication in the protocol, we show that i) one can simulate the protocol using order I^A + (C^3 * I^B)^(1/4) * log(C) + (C * I^B)^(1/2) * log(C) bits of communication, ii) one can simulate the protocol using order I^A * 2^(O(I^B)) bits of communication The first result gives the best known bound on the complexity of a simulation when I^A >> I^B,C^(3/4). The second gives the best known bound when I^B << log C. In addition we show that if a function is computed by a protocol with asymmetric information complexity, then the inputs must have a large, nearly monochromatic rectangle of the right dimensions, a fact that is useful for proving lower bounds on lopsided communication problems.

Cite as

Sivaramakrishnan Natarajan Ramamoorthy and Anup Rao. How to Compress Asymmetric Communication. In 30th Conference on Computational Complexity (CCC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 33, pp. 102-123, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{natarajanramamoorthy_et_al:LIPIcs.CCC.2015.102,
  author =	{Natarajan Ramamoorthy, Sivaramakrishnan and Rao, Anup},
  title =	{{How to Compress Asymmetric Communication}},
  booktitle =	{30th Conference on Computational Complexity (CCC 2015)},
  pages =	{102--123},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-81-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{33},
  editor =	{Zuckerman, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2015.102},
  URN =		{urn:nbn:de:0030-drops-50679},
  doi =		{10.4230/LIPIcs.CCC.2015.102},
  annote =	{Keywords: Communication Complexity, Interactive Compression, Information Complexity}
}
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