17 Search Results for "Ben-Basat, Ran"


Document
Static vs. Adaptive Security in Perfect MPC: A Separation and the Adaptive Security of BGW

Authors: Gilad Asharov, Ran Cohen, and Oren Shochat

Published in: LIPIcs, Volume 230, 3rd Conference on Information-Theoretic Cryptography (ITC 2022)


Abstract
Adaptive security is a highly desirable property in the design of secure protocols. It tolerates adversaries that corrupt parties as the protocol proceeds, as opposed to static security where the adversary corrupts the parties at the onset of the execution. The well-accepted folklore is that static and adaptive securities are equivalent for perfectly secure protocols. Indeed, this folklore is backed up with a transformation by Canetti et al. (EUROCRYPT'01), showing that any perfectly secure protocol that is statically secure and satisfies some basic requirements is also adaptively secure. Yet, the transformation results in an adaptively secure protocol with inefficient simulation (i.e., where the simulator might run in super-polynomial time even if the adversary runs just in polynomial time). Inefficient simulation is problematic when using the protocol as a sub-routine in the computational setting. Our main question is whether an alternative efficient transformation from static to adaptive security exists. We show an inherent difficulty in achieving this goal generically. In contrast to the folklore, we present a protocol that is perfectly secure with efficient static simulation (therefore also adaptively secure with inefficient simulation), but for which efficient adaptive simulation does not exist (assuming the existence of one-way permutations). In addition, we prove that the seminal protocol of Ben-Or, Goldwasser and Wigderson (STOC'88) is secure against adaptive, semi-honest corruptions with efficient simulation. Previously, adaptive security of the protocol, as is, was only known either for a restricted class of circuits, or for all circuits but with inefficient simulation.

Cite as

Gilad Asharov, Ran Cohen, and Oren Shochat. Static vs. Adaptive Security in Perfect MPC: A Separation and the Adaptive Security of BGW. In 3rd Conference on Information-Theoretic Cryptography (ITC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 230, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{asharov_et_al:LIPIcs.ITC.2022.15,
  author =	{Asharov, Gilad and Cohen, Ran and Shochat, Oren},
  title =	{{Static vs. Adaptive Security in Perfect MPC: A Separation and the Adaptive Security of BGW}},
  booktitle =	{3rd Conference on Information-Theoretic Cryptography (ITC 2022)},
  pages =	{15:1--15:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-238-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{230},
  editor =	{Dachman-Soled, Dana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2022.15},
  URN =		{urn:nbn:de:0030-drops-164933},
  doi =		{10.4230/LIPIcs.ITC.2022.15},
  annote =	{Keywords: secure multiparty computation, perfect security, adaptive security, BGW protocol}
}
Document
Track A: Algorithms, Complexity and Games
How to Send a Real Number Using a Single Bit (And Some Shared Randomness)

Authors: Ran Ben Basat, Michael Mitzenmacher, and Shay Vargaftik

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


Abstract
We consider the fundamental problem of communicating an estimate of a real number x ∈ [0,1] using a single bit. A sender that knows x chooses a value X ∈ {0,1} to transmit. In turn, a receiver estimates x based on the value of X. The goal is to minimize the cost, defined as the worst-case (over the choice of x) expected squared error. We first overview common biased and unbiased estimation approaches and prove their optimality when no shared randomness is allowed. We then show how a small amount of shared randomness, which can be as low as a single bit, reduces the cost in both cases. Specifically, we derive lower bounds on the cost attainable by any algorithm with unrestricted use of shared randomness and propose optimal and near-optimal solutions that use a small number of shared random bits. Finally, we discuss open problems and future directions.

Cite as

Ran Ben Basat, Michael Mitzenmacher, and Shay Vargaftik. How to Send a Real Number Using a Single Bit (And Some Shared Randomness). In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 25:1-25:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{benbasat_et_al:LIPIcs.ICALP.2021.25,
  author =	{Ben Basat, Ran and Mitzenmacher, Michael and Vargaftik, Shay},
  title =	{{How to Send a Real Number Using a Single Bit (And Some Shared Randomness)}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{25:1--25:20},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.25},
  URN =		{urn:nbn:de:0030-drops-140942},
  doi =		{10.4230/LIPIcs.ICALP.2021.25},
  annote =	{Keywords: Randomized Algorithms, Approximation Algorithms, Shared Randomness, Distributed Protocols, Estimation, Subtractive Dithering}
}
Document
Optimal Distributed Covering Algorithms

Authors: Ran Ben-Basat, Guy Even, Ken-ichi Kawarabayashi, and Gregory Schwartzman

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


Abstract
We present a time-optimal deterministic distributed algorithm for approximating a minimum weight vertex cover in hypergraphs of rank f. This problem is equivalent to the Minimum Weight Set Cover problem in which the frequency of every element is bounded by f. The approximation factor of our algorithm is (f+epsilon). Let Delta denote the maximum degree in the hypergraph. Our algorithm runs in the congest model and requires O(log{Delta} / log log Delta) rounds, for constants epsilon in (0,1] and f in N^+. This is the first distributed algorithm for this problem whose running time does not depend on the vertex weights nor the number of vertices. Thus adding another member to the exclusive family of provably optimal distributed algorithms. For constant values of f and epsilon, our algorithm improves over the (f+epsilon)-approximation algorithm of [Fabian Kuhn et al., 2006] whose running time is O(log Delta + log W), where W is the ratio between the largest and smallest vertex weights in the graph. Our algorithm also achieves an f-approximation for the problem in O(f log n) rounds, improving over the classical result of [Samir Khuller et al., 1994] that achieves a running time of O(f log^2 n). Finally, for weighted vertex cover (f=2) our algorithm achieves a deterministic running time of O(log n), matching the randomized previously best result of [Koufogiannakis and Young, 2011]. We also show that integer covering-programs can be reduced to the Minimum Weight Set Cover problem in the distributed setting. This allows us to achieve an (f+epsilon)-approximate integral solution in O((1+f/log n)* ((log Delta)/(log log Delta) + (f * log M)^{1.01}* log epsilon^{-1}* (log Delta)^{0.01})) rounds, where f bounds the number of variables in a constraint, Delta bounds the number of constraints a variable appears in, and M=max {1, ceil[1/a_{min}]}, where a_{min} is the smallest normalized constraint coefficient. This improves over the results of [Fabian Kuhn et al., 2006] for the integral case, which combined with rounding achieves the same guarantees in O(epsilon^{-4}* f^4 * log f * log(M * Delta)) rounds.

Cite as

Ran Ben-Basat, Guy Even, Ken-ichi Kawarabayashi, and Gregory Schwartzman. Optimal Distributed Covering Algorithms. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 5:1-5:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{benbasat_et_al:LIPIcs.DISC.2019.5,
  author =	{Ben-Basat, Ran and Even, Guy and Kawarabayashi, Ken-ichi and Schwartzman, Gregory},
  title =	{{Optimal Distributed Covering Algorithms}},
  booktitle =	{33rd International Symposium on Distributed Computing (DISC 2019)},
  pages =	{5:1--5:15},
  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.2019.5},
  URN =		{urn:nbn:de:0030-drops-113129},
  doi =		{10.4230/LIPIcs.DISC.2019.5},
  annote =	{Keywords: Distributed Algorithms, Approximation Algorithms, Vertex Cover, Set Cover}
}
Document
Parameterized Distributed Algorithms

Authors: Ran Ben-Basat, Ken-ichi Kawarabayashi, and Gregory Schwartzman

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


Abstract
In this work, we initiate a thorough study of graph optimization problems parameterized by the output size in the distributed setting. In such a problem, an algorithm decides whether a solution of size bounded by k exists and if so, it finds one. We study fundamental problems, including Minimum Vertex Cover (MVC), Maximum Independent Set (MaxIS), Maximum Matching (MaxM), and many others, in both the LOCAL and CONGEST distributed computation models. We present lower bounds for the round complexity of solving parameterized problems in both models, together with optimal and near-optimal upper bounds. Our results extend beyond the scope of parameterized problems. We show that any LOCAL (1+epsilon)-approximation algorithm for the above problems must take Omega(epsilon^{-1}) rounds. Joined with the (epsilon^{-1}log n)^{O(1)} rounds algorithm of [Ghaffari et al., 2017] and the Omega (sqrt{(log n)/(log log n)}) lower bound of [Fabian Kuhn et al., 2016], the lower bounds match the upper bound up to polynomial factors in both parameters. We also show that our parameterized approach reduces the runtime of exact and approximate CONGEST algorithms for MVC and MaxM if the optimal solution is small, without knowing its size beforehand. Finally, we propose the first o(n^2) rounds CONGEST algorithms that approximate MVC within a factor strictly smaller than 2.

Cite as

Ran Ben-Basat, Ken-ichi Kawarabayashi, and Gregory Schwartzman. Parameterized Distributed Algorithms. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{benbasat_et_al:LIPIcs.DISC.2019.6,
  author =	{Ben-Basat, Ran and Kawarabayashi, Ken-ichi and Schwartzman, Gregory},
  title =	{{Parameterized Distributed Algorithms}},
  booktitle =	{33rd International Symposium on Distributed Computing (DISC 2019)},
  pages =	{6:1--6:16},
  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.2019.6},
  URN =		{urn:nbn:de:0030-drops-113135},
  doi =		{10.4230/LIPIcs.DISC.2019.6},
  annote =	{Keywords: Distributed Algorithms, Approximation Algorithms, Parameterized Algorithms}
}
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-dev.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
Track A: Algorithms, Complexity and Games
Towards Optimal Depth Reductions for Syntactically Multilinear Circuits

Authors: Mrinal Kumar, Rafael Oliveira, and Ramprasad Saptharishi

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


Abstract
We show that any n-variate polynomial computable by a syntactically multilinear circuit of size poly(n) can be computed by a depth-4 syntactically multilinear (Sigma Pi Sigma Pi) circuit of size at most exp ({O (sqrt{n log n})}). For degree d = omega(n/log n), this improves upon the upper bound of exp ({O(sqrt{d}log n)}) obtained by Tavenas [Sébastien Tavenas, 2015] for general circuits, and is known to be asymptotically optimal in the exponent when d < n^{epsilon} for a small enough constant epsilon. Our upper bound matches the lower bound of exp ({Omega (sqrt{n log n})}) proved by Raz and Yehudayoff [Ran Raz and Amir Yehudayoff, 2009], and thus cannot be improved further in the exponent. Our results hold over all fields and also generalize to circuits of small individual degree. More generally, we show that an n-variate polynomial computable by a syntactically multilinear circuit of size poly(n) can be computed by a syntactically multilinear circuit of product-depth Delta of size at most exp inparen{O inparen{Delta * (n/log n)^{1/Delta} * log n}}. It follows from the lower bounds of Raz and Yehudayoff [Ran Raz and Amir Yehudayoff, 2009] that in general, for constant Delta, the exponent in this upper bound is tight and cannot be improved to o inparen{inparen{n/log n}^{1/Delta}* log n}.

Cite as

Mrinal Kumar, Rafael Oliveira, and Ramprasad Saptharishi. Towards Optimal Depth Reductions for Syntactically Multilinear Circuits. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 78:1-78:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{kumar_et_al:LIPIcs.ICALP.2019.78,
  author =	{Kumar, Mrinal and Oliveira, Rafael and Saptharishi, Ramprasad},
  title =	{{Towards Optimal Depth Reductions for Syntactically Multilinear Circuits}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{78:1--78:15},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.78},
  URN =		{urn:nbn:de:0030-drops-106548},
  doi =		{10.4230/LIPIcs.ICALP.2019.78},
  annote =	{Keywords: arithmetic circuits, multilinear circuits, depth reduction, lower bounds}
}
Document
Approximate Query Processing over Static Sets and Sliding Windows

Authors: Ran Ben Basat, Seungbum Jo, Srinivasa Rao Satti, and Shubham Ugare

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)


Abstract
Indexing of static and dynamic sets is fundamental to a large set of applications such as information retrieval and caching. Denoting the characteristic vector of the set by B, we consider the problem of encoding sets and multisets to support approximate versions of the operations rank(i) (i.e., computing sum_{j <= i} B[j]) and select(i) (i.e., finding min{p|rank(p) >= i}) queries. We study multiple types of approximations (allowing an error in the query or the result) and present lower bounds and succinct data structures for several variants of the problem. We also extend our model to sliding windows, in which we process a stream of elements and compute suffix sums. This is a generalization of the window summation problem that allows the user to specify the window size at query time. Here, we provide an algorithm that supports updates and queries in constant time while requiring just (1+o(1)) factor more space than the fixed-window summation algorithms.

Cite as

Ran Ben Basat, Seungbum Jo, Srinivasa Rao Satti, and Shubham Ugare. Approximate Query Processing over Static Sets and Sliding Windows. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 54:1-54:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{benbasat_et_al:LIPIcs.ISAAC.2018.54,
  author =	{Ben Basat, Ran and Jo, Seungbum and Satti, Srinivasa Rao and Ugare, Shubham},
  title =	{{Approximate Query Processing over Static Sets and Sliding Windows}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{54:1--54:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.54},
  URN =		{urn:nbn:de:0030-drops-100027},
  doi =		{10.4230/LIPIcs.ISAAC.2018.54},
  annote =	{Keywords: Streaming, Algorithms, Sliding window, Lower bounds}
}
Document
A Lower Bound for Adaptively-Secure Collective Coin-Flipping Protocols

Authors: Yael Tauman Kalai, Ilan Komargodski, and Ran Raz

Published in: LIPIcs, Volume 121, 32nd International Symposium on Distributed Computing (DISC 2018)


Abstract
In 1985, Ben-Or and Linial (Advances in Computing Research '89) introduced the collective coin-flipping problem, where n parties communicate via a single broadcast channel and wish to generate a common random bit in the presence of adaptive Byzantine corruptions. In this model, the adversary can decide to corrupt a party in the course of the protocol as a function of the messages seen so far. They showed that the majority protocol, in which each player sends a random bit and the output is the majority value, tolerates O(sqrt n) adaptive corruptions. They conjectured that this is optimal for such adversaries. We prove that the majority protocol is optimal (up to a poly-logarithmic factor) among all protocols in which each party sends a single, possibly long, message. Previously, such a lower bound was known for protocols in which parties are allowed to send only a single bit (Lichtenstein, Linial, and Saks, Combinatorica '89), or for symmetric protocols (Goldwasser, Kalai, and Park, ICALP '15).

Cite as

Yael Tauman Kalai, Ilan Komargodski, and Ran Raz. A Lower Bound for Adaptively-Secure Collective Coin-Flipping Protocols. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 34:1-34:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{taumankalai_et_al:LIPIcs.DISC.2018.34,
  author =	{Tauman Kalai, Yael and Komargodski, Ilan and Raz, Ran},
  title =	{{A Lower Bound for Adaptively-Secure Collective Coin-Flipping Protocols}},
  booktitle =	{32nd International Symposium on Distributed Computing (DISC 2018)},
  pages =	{34:1--34:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-092-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{121},
  editor =	{Schmid, Ulrich and Widder, Josef},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.34},
  URN =		{urn:nbn:de:0030-drops-98230},
  doi =		{10.4230/LIPIcs.DISC.2018.34},
  annote =	{Keywords: Coin flipping, adaptive corruptions, byzantine faults, lower bound}
}
Document
Give Me Some Slack: Efficient Network Measurements

Authors: Ran Ben Basat, Gil Einziger, and Roy Friedman

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)


Abstract
Many networking applications require timely access to recent network measurements, which can be captured using a sliding window model. Maintaining such measurements is a challenging task due to the fast line speed and scarcity of fast memory in routers. In this work, we study the impact of allowing slack in the window size on the asymptotic requirements of sliding window problems. That is, the algorithm can dynamically adjust the window size between W and W(1+tau) where tau is a small positive parameter. We demonstrate this model's attractiveness by showing that it enables efficient algorithms to problems such as Maximum and General-Summing that require Omega(W) bits even for constant factor approximations in the exact sliding window model. Additionally, for problems that admit sub-linear approximation algorithms such as Basic-Summing and Count-Distinct, the slack model enables a further asymptotic improvement. The main focus of the paper is on the widely studied Basic-Summing problem of computing the sum of the last W integers from {0,1 ...,R} in a stream. While it is known that Omega(W log R) bits are needed in the exact window model, we show that approximate windows allow an exponential space reduction for constant tau. Specifically, for tau=Theta(1), we present a space lower bound of Omega(log(RW)) bits. Additionally, we show an Omega(log (W/epsilon)) lower bound for RW epsilon additive approximations and a Omega(log (W/epsilon)+log log R) bits lower bound for (1+epsilon) multiplicative approximations. Our work is the first to study this problem in the exact and additive approximation settings. For all settings, we provide memory optimal algorithms that operate in worst case constant time. This strictly improves on the work of [Mayur Datar et al., 2002] for (1+epsilon)-multiplicative approximation that requires O(epsilon^(-1) log(RW)log log (RW)) space and performs updates in O(log (RW)) worst case time. Finally, we show asymptotic improvements for the Count-Distinct, General-Summing and Maximum problems.

Cite as

Ran Ben Basat, Gil Einziger, and Roy Friedman. Give Me Some Slack: Efficient Network Measurements. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 34:1-34:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{benbasat_et_al:LIPIcs.MFCS.2018.34,
  author =	{Ben Basat, Ran and Einziger, Gil and Friedman, Roy},
  title =	{{Give Me Some Slack: Efficient Network Measurements}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{34:1--34:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.34},
  URN =		{urn:nbn:de:0030-drops-96165},
  doi =		{10.4230/LIPIcs.MFCS.2018.34},
  annote =	{Keywords: Streaming, Network Measurements, Statistics, Lower Bounds}
}
Document
Brief Announcement
Brief Announcement: Give Me Some Slack: Efficient Network Measurements

Authors: Ran Ben Basat, Gil Einziger, and Roy Friedman

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)


Abstract
Many networking applications require timely access to recent network measurements, which can be captured using a sliding window model. Maintaining such measurements is a challenging task due to the fast line speed and scarcity of fast memory in routers. In this work, we study the impact of allowing slack in the window size on the asymptotic requirements of sliding window problems. That is, the algorithm can dynamically adjust the window size between W and W(1+tau) where tau is a small positive parameter. We demonstrate this model's attractiveness by showing that it enables efficient algorithms to problems such as Maximum and General-Summing that require Omega(W) bits even for constant factor approximations in the exact sliding window model. Additionally, for problems that admit sub-linear approximation algorithms such as Basic-Summing and Count-Distinct, the slack model enables a further asymptotic improvement. The main focus of our paper [{Ben Basat} et al., 2017] is on the widely studied Basic-Summing problem of computing the sum of the last W integers from {0,1 ...,R} in a stream. While it is known that Omega(W log{R}) bits are needed in the exact window model, we show that approximate windows allow an exponential space reduction for constant tau. Specifically, for tau=Theta(1), we present a space lower bound of Omega(log(RW)) bits. Additionally, we show an Omega(log ({W/epsilon})) lower bound for RW epsilon additive approximations and a Omega(log ({W/epsilon})+log log{R}) bits lower bound for (1+epsilon) multiplicative approximations. Our work is the first to study this problem in the exact and additive approximation settings. For all settings, we provide memory optimal algorithms that operate in worst case constant time. This strictly improves on the work of [Mayur Datar et al., 2002] for (1+epsilon)-multiplicative approximation that requires O(epsilon^{-1} log ({RW})log log ({RW})) space and performs updates in O(log ({RW})) worst case time. Finally, we show asymptotic improvements for the Count-Distinct, General-Summing and Maximum problems.

Cite as

Ran Ben Basat, Gil Einziger, and Roy Friedman. Brief Announcement: Give Me Some Slack: Efficient Network Measurements. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 163:1-163:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{benbasat_et_al:LIPIcs.ICALP.2018.163,
  author =	{Ben Basat, Ran and Einziger, Gil and Friedman, Roy},
  title =	{{Brief Announcement: Give Me Some Slack: Efficient Network Measurements}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{163:1--163:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.163},
  URN =		{urn:nbn:de:0030-drops-91672},
  doi =		{10.4230/LIPIcs.ICALP.2018.163},
  annote =	{Keywords: Streaming, Algorithms, Sliding window, Lower bounds}
}
Document
Unbalancing Sets and an Almost Quadratic Lower Bound for Syntactically Multilinear Arithmetic Circuits

Authors: Noga Alon, Mrinal Kumar, and Ben Lee Volk

Published in: LIPIcs, Volume 102, 33rd Computational Complexity Conference (CCC 2018)


Abstract
We prove a lower bound of Omega(n^2/log^2 n) on the size of any syntactically multilinear arithmetic circuit computing some explicit multilinear polynomial f(x_1, ..., x_n). Our approach expands and improves upon a result of Raz, Shpilka and Yehudayoff ([Ran Raz et al., 2008]), who proved a lower bound of Omega(n^{4/3}/log^2 n) for the same polynomial. Our improvement follows from an asymptotically optimal lower bound for a generalized version of Galvin's problem in extremal set theory.

Cite as

Noga Alon, Mrinal Kumar, and Ben Lee Volk. Unbalancing Sets and an Almost Quadratic Lower Bound for Syntactically Multilinear Arithmetic Circuits. In 33rd Computational Complexity Conference (CCC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 102, pp. 11:1-11:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{alon_et_al:LIPIcs.CCC.2018.11,
  author =	{Alon, Noga and Kumar, Mrinal and Volk, Ben Lee},
  title =	{{Unbalancing Sets and an Almost Quadratic Lower Bound for Syntactically Multilinear Arithmetic Circuits}},
  booktitle =	{33rd Computational Complexity Conference (CCC 2018)},
  pages =	{11:1--11:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-069-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{102},
  editor =	{Servedio, Rocco A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2018.11},
  URN =		{urn:nbn:de:0030-drops-88799},
  doi =		{10.4230/LIPIcs.CCC.2018.11},
  annote =	{Keywords: Algebraic Complexity, Multilinear Circuits, Circuit Lower Bounds}
}
Document
Round-Preserving Parallel Composition of Probabilistic-Termination Cryptographic Protocols

Authors: Ran Cohen, Sandro Coretti, Juan Garay, and Vassilis Zikas

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)


Abstract
An important benchmark for multi-party computation protocols (MPC) is their round complexity. For several important MPC tasks, (tight) lower bounds on the round complexity are known. However, for some of these tasks, such as broadcast, the lower bounds can be circumvented when the termination round of every party is not a priori known, and simultaneous termination is not guaranteed. Protocols with this property are called probabilistic-termination (PT) protocols. Running PT protocols in parallel affects the round complexity of the resulting protocol in somewhat unexpected ways. For instance, an execution of m protocols with constant expected round complexity might take O(log m) rounds to complete. In a seminal work, Ben-Or and El-Yaniv (Distributed Computing '03) developed a technique for parallel execution of arbitrarily many broadcast protocols, while preserving expected round complexity. More recently, Cohen et al. (CRYPTO '16) devised a framework for universal composition of PT protocols, and provided the first composable parallel-broadcast protocol with a simulation-based proof. These constructions crucially rely on the fact that broadcast is ``privacy free,'' and do not generalize to arbitrary protocols in a straightforward way. This raises the question of whether it is possible to execute arbitrary PT protocols in parallel, without increasing the round complexity. In this paper we tackle this question and provide both feasibility and infeasibility results. We construct a round-preserving protocol compiler, secure against a dishonest minority of actively corrupted parties, that compiles arbitrary protocols into a protocol realizing their parallel composition, while having a black-box access to the underlying protocols. Furthermore, we prove that the same cannot be achieved, using known techniques, given only black-box access to the functionalities realized by the protocols, unless merely security against semi-honest corruptions is required, for which case we provide a protocol.

Cite as

Ran Cohen, Sandro Coretti, Juan Garay, and Vassilis Zikas. Round-Preserving Parallel Composition of Probabilistic-Termination Cryptographic Protocols. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 37:1-37:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{cohen_et_al:LIPIcs.ICALP.2017.37,
  author =	{Cohen, Ran and Coretti, Sandro and Garay, Juan and Zikas, Vassilis},
  title =	{{Round-Preserving Parallel Composition of Probabilistic-Termination Cryptographic Protocols}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{37:1--37:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.37},
  URN =		{urn:nbn:de:0030-drops-74124},
  doi =		{10.4230/LIPIcs.ICALP.2017.37},
  annote =	{Keywords: Cryptographic protocols, secure multi-party computation, broadcast.}
}
Document
Efficient Summing over Sliding Windows

Authors: Ran Ben Basat, Gil Einziger, Roy Friedman, and Yaron Kassner

Published in: LIPIcs, Volume 53, 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)


Abstract
This paper considers the problem of maintaining statistic aggregates over the last W elements of a data stream. First, the problem of counting the number of 1's in the last W bits of a binary stream is considered. A lower bound of Omega(1/epsilon + log(W)) memory bits for Wepsilon-additive approximations is derived. This is followed by an algorithm whose memory consumption is O(1/epsilon + log(W)) bits, indicating that the algorithm is optimal and that the bound is tight. Next, the more general problem of maintaining a sum of the last W integers, each in the range of {0, 1, ..., R}, is addressed. The paper shows that approximating the sum within an additive error of RW epsilon can also be done using Theta(1/epsilon + log(W)) bits for epsilon = Omega(1/W). For epsilon = o(1/W), we present a succinct algorithm which uses B(1 + o(1)) bits, where B = Theta(W*log(1/(W*epsilon))) is the derived lower bound. We show that all lower bounds generalize to randomized algorithms as well. All algorithms process new elements and answer queries in O(1) worst-case time.

Cite as

Ran Ben Basat, Gil Einziger, Roy Friedman, and Yaron Kassner. Efficient Summing over Sliding Windows. In 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 53, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{benbasat_et_al:LIPIcs.SWAT.2016.11,
  author =	{Ben Basat, Ran and Einziger, Gil and Friedman, Roy and Kassner, Yaron},
  title =	{{Efficient Summing over Sliding Windows}},
  booktitle =	{15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)},
  pages =	{11:1--11:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-011-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{53},
  editor =	{Pagh, Rasmus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2016.11},
  URN =		{urn:nbn:de:0030-drops-60241},
  doi =		{10.4230/LIPIcs.SWAT.2016.11},
  annote =	{Keywords: Streaming, Statistics, Lower Bounds}
}
Document
Nearly Optimal Separations Between Communication (or Query) Complexity and Partitions

Authors: Andris Ambainis, Martins Kokainis, and Robin Kothari

Published in: LIPIcs, Volume 50, 31st Conference on Computational Complexity (CCC 2016)


Abstract
We show a nearly quadratic separation between deterministic communication complexity and the logarithm of the partition number, which is essentially optimal. This improves upon a recent power 1.5 separation of Göös, Pitassi, and Watson (FOCS 2015). In query complexity, we establish a nearly quadratic separation between deterministic (and even randomized) query complexity and subcube partition complexity, which is also essentially optimal. We also establish a nearly power 1.5 separation between quantum query complexity and subcube partition complexity, the first superlinear separation between the two measures. Lastly, we show a quadratic separation between quantum query complexity and one-sided subcube partition complexity. Our query complexity separations use the recent cheat sheet framework of Aaronson, Ben-David, and Kothari. Our query functions are built up in stages by alternating function composition with the cheat sheet construction. The communication complexity separation follows from "lifting" the query separation to communication complexity.

Cite as

Andris Ambainis, Martins Kokainis, and Robin Kothari. Nearly Optimal Separations Between Communication (or Query) Complexity and Partitions. In 31st Conference on Computational Complexity (CCC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 50, pp. 4:1-4:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{ambainis_et_al:LIPIcs.CCC.2016.4,
  author =	{Ambainis, Andris and Kokainis, Martins and Kothari, Robin},
  title =	{{Nearly Optimal Separations Between Communication (or Query) Complexity and Partitions}},
  booktitle =	{31st Conference on Computational Complexity (CCC 2016)},
  pages =	{4:1--4:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-008-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{50},
  editor =	{Raz, Ran},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2016.4},
  URN =		{urn:nbn:de:0030-drops-58471},
  doi =		{10.4230/LIPIcs.CCC.2016.4},
  annote =	{Keywords: Query Complexity, Communication Complexity, Subcube Partition Complexity, Partition Bound}
}
Document
Lower Bounds for Constant Query Affine-Invariant LCCs and LTCs

Authors: Arnab Bhattacharyya and Sivakanth Gopi

Published in: LIPIcs, Volume 50, 31st Conference on Computational Complexity (CCC 2016)


Abstract
Affine-invariant codes are codes whose coordinates form a vector space over a finite field and which are invariant under affine transformations of the coordinate space. They form a natural, well-studied class of codes; they include popular codes such as Reed-Muller and Reed-Solomon. A particularly appealing feature of affine-invariant codes is that they seem well-suited to admit local correctors and testers. In this work, we give lower bounds on the length of locally correctable and locally testable affine-invariant codes with constant query complexity. We show that if a code C subset Sigma^{K^n} is an r-query locally correctable code (LCC), where K is a finite field and Sigma is a finite alphabet, then the number of codewords in C is at most exp(O_{K, r, |Sigma|}(n^{r-1})). Also, we show that if C subset Sigma^{K^n} is an r-query locally testable code (LTC), then the number of codewords in C is at most \exp(O_{K, r, |Sigma|}(n^{r-2})). The dependence on n in these bounds is tight for constant-query LCCs/LTCs, since Guo, Kopparty and Sudan (ITCS 2013) construct affine-invariant codes via lifting that have the same asymptotic tradeoffs. Note that our result holds for non-linear codes, whereas previously, Ben-Sasson and Sudan (RANDOM 2011) assumed linearity to derive similar results. Our analysis uses higher-order Fourier analysis. In particular, we show that the codewords corresponding to an affine-invariant LCC/LTC must be far from each other with respect to Gowers norm of an appropriate order. This then allows us to bound the number of codewords, using known decomposition theorems which approximate any bounded function in terms of a finite number of low-degree non-classical polynomials, upto a small error in the Gowers norm.

Cite as

Arnab Bhattacharyya and Sivakanth Gopi. Lower Bounds for Constant Query Affine-Invariant LCCs and LTCs. In 31st Conference on Computational Complexity (CCC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 50, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{bhattacharyya_et_al:LIPIcs.CCC.2016.12,
  author =	{Bhattacharyya, Arnab and Gopi, Sivakanth},
  title =	{{Lower Bounds for Constant Query Affine-Invariant LCCs and LTCs}},
  booktitle =	{31st Conference on Computational Complexity (CCC 2016)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-008-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{50},
  editor =	{Raz, Ran},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2016.12},
  URN =		{urn:nbn:de:0030-drops-58400},
  doi =		{10.4230/LIPIcs.CCC.2016.12},
  annote =	{Keywords: Locally correctable code, Locally testable code, Affine Invariance, Gowers uniformity norm}
}
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