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Noise Tolerance of Expanders and Sublinear Expansion Reconstruction

Satyen Kale, Yuval Peres, C. Seshadhri
2013 SIAM journal on computing (Print)  
Noise-tolerance of Markov Chains First, we discuss our theorem about the noise-tolerance of Markov chains. Later, we apply this to our setting of expansion reconstruction.  ...  In Section 2, we describe our results on the noise-tolerance of expanders in a general setting.  ...  This procedure will output all the neighbors of an input vertex u on the reconstructed graph and involves calling Remove on O(d) edges. Reconstruct Input: Vertex v ∈ V . 1.  ... 
doi:10.1137/110837863 fatcat:c3f7tk7mmvdblejo6cmuw5uqjq

Noise Tolerance of Expanders and Sublinear Expander Reconstruction

Satyen Kale, Yuval Peres, C. Seshadhri
2008 2008 49th Annual IEEE Symposium on Foundations of Computer Science  
We consider the problem of online sublinear expander reconstruction and its relation to random walks in "noisy" expanders.  ...  We also design sublinear time procedures to distinguish vertices of the expander part from those in the noise part, and use this procedure in the reconstruction algorithm.  ...  Acknowledgements The authors would like to thank Reid Andersen, Itai Benjamini, Bernard Chazelle, Fan Chung, László Lovász, Eyal Lubetzky, Elchanan Mossel, Dana Randall and Shang-Hua Teng for helpful discussions  ... 
doi:10.1109/focs.2008.65 dblp:conf/focs/KalePS08 fatcat:juvccrgeijgnlpy6m3l53ue77m

Deterministic Heavy Hitters with Sublinear Query Time [article]

Yi Li, Vasileios Nakos
2018 arXiv   pre-print
Along the way, we also give sublinear time algorithms for the closely related problems of combinatorial group testing and $\ell_1/\ell_1$ compressed sensing, matching the space usage of previous (super  ...  We give the first deterministic linear sketch that has $O(\epsilon^{-2} \log n \cdot \log^*(\epsilon^{-1}))$ rows and answers queries in sublinear time.  ...  Reed-Solomon code) that can tolerate up to δ 2 fraction of error, we shall recoverm i,r in entirety.  ... 
arXiv:1712.01971v2 fatcat:cu647vmksvfxjkkdkd6np45qfm

Combining geometry and combinatorics: A unified approach to sparse signal recovery [article]

R. Berinde, A. C. Gilbert, P. Indyk, H. Karloff, M. J. Strauss
2008 arXiv   pre-print
, are superior in either the number of measurements or in noise tolerance.  ...  The unifying elements are the adjacency matrices of high-quality unbalanced expanders.  ...  With judicious choice of unbalanced expander parameters, we have (1 − ρ ′ )ℓ isolated spikes corrupted by a small amount of noise.  ... 
arXiv:0804.4666v1 fatcat:crswkkfjaff5dj3lqxnz5drjl4

Rapidly Computing Sparse Legendre Expansions via Sparse Fourier Transforms [article]

Xianfeng Hu, Mark Iwen, Hyejin Kim
2016 arXiv   pre-print
When $s \ll N$ these algorithms exhibit sublinear runtime complexities in $N$, as opposed to traditional $\Omega(N \log N)$-time methods for computing all of the first $N$ Legendre coefficients of $f$.  ...  In this paper we propose a general strategy for rapidly computing sparse Legendre expansions.  ...  Acknowledgements The authors would like to thank Aditya Viswanathan for many helpful suggestions and discussions during the writing of this paper.  ... 
arXiv:1508.04758v2 fatcat:xazxxaol5fg4vb4c53r4uyet4a

Efficient and Robust Compressed Sensing Using Optimized Expander Graphs

Sina Jafarpour, Weiyu Xu, Babak Hassibi, Robert Calderbank
2009 IEEE Transactions on Information Theory  
We also show that by tolerating a small penalty on the number of measurements, and not on the number of recovery iterations, one can use the efficient construction of a family of expander graphs to come  ...  In this paper, we improve upon this result by considering expander graphs with expansion coefficient beyond 3 4 and show that, with the same number of measurements, only O(k) recovery iterations are required  ...  ACKNOWLEDGMENT The authors would like to thank Piotr Indyk, Justin Romberg, the readers and the anonymous reviewers of the paper for their insights and suggestions.  ... 
doi:10.1109/tit.2009.2025528 fatcat:uafhw7hjqfet3bhb72hpuaaawq

For-All Sparse Recovery in Near-Optimal Time

Anna C. Gilbert, Yi Li, Ely Porat, Martin J. Strauss
2017 ACM Transactions on Algorithms  
Portions of the message m ′ i correspond to repetitions of the hashing and we use a regular expander graph to encode the linkages among these portions.  ...  The best existing sublinear algorithm by Porat and Strauss (SODA'12) uses O(ǫ −3 k log(N/k)) measurements and runs in time O(k 1−α N α ) for any constant α > 0.  ...  We can choose the hidden constants in the expander parameters such that β 1 ≥ 1 − ζ and β 2 matches the error tolerance of the coding scheme we described in Lemma 17, where ζ is the parameter we set in  ... 
doi:10.1145/3039872 fatcat:jlu7zre42fhdvc7bymmhjufgc4

For-All Sparse Recovery in Near-Optimal Time [chapter]

Anna C. Gilbert, Yi Li, Ely Porat, Martin J. Strauss
2014 Lecture Notes in Computer Science  
Portions of the message m ′ i correspond to repetitions of the hashing and we use a regular expander graph to encode the linkages among these portions.  ...  The best existing sublinear algorithm by Porat and Strauss (SODA'12) uses O(ǫ −3 k log(N/k)) measurements and runs in time O(k 1−α N α ) for any constant α > 0.  ...  We can choose the hidden constants in the expander parameters such that β 1 ≥ 1 − ζ and β 2 matches the error tolerance of the coding scheme we described in Lemma 17, where ζ is the parameter we set in  ... 
doi:10.1007/978-3-662-43948-7_45 fatcat:rxqeeqq5lngb7n3bkxjffwptqi

Learning Sparse Polynomial Functions [chapter]

Alexandr Andoni, Rina Panigrahy, Gregory Valiant, Li Zhang
2013 Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms  
In particular, for some unknown polynomial f ( x) of degree-d and k monomials, we show how to reconstruct f , within error , given only a set of examplesx i drawn uniformly from the n-dimensional cube  ...  The runtime of our algorithm is polynomial in n, k, 1/ and C d where C d depends only on d.  ...  We can expand the product and check the coefficient of H 2t1,2t2,··· ,2tr,2t,0,··· ,0 in the above expansion.  ... 
doi:10.1137/1.9781611973402.37 dblp:conf/soda/AndoniPV014 fatcat:uwsyic4rarbl3btcftvtisopiq

A Survey on Lightweight Entity Authentication with Strong PUFs

Jeroen Delvaux, Roel Peeters, Dawu Gu, Ingrid Verbauwhede
2015 ACM Computing Surveys  
In this work, we review nineteen proposals in chronological order: from the original strong PUF proposal (2001) to the more complicated noise bifurcation and system of PUF proposals (2014).  ...  The assessment is aided by a unified notation and a transparent framework of PUF protocol requirements. The work comprehends a sequel on our prior CHES 2014 manuscript 1 .  ...  Able to Handle Noisiness (#3) Noisiness of the PUF responses should be taken into account. One can employ either one of two approaches: error correction and error tolerance.  ... 
doi:10.1145/2818186 fatcat:lzn6sb3g55a5rkdmunilfz3wtq

Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals

Joel A. Tropp, Jason N. Laska, Marco F. Duarte, Justin K. Romberg, Richard G. Baraniuk
2010 IEEE Transactions on Information Theory  
Let K denote the total number of frequencies in the signal, and let W denote its bandlimit in Hz.  ...  Simulations suggest that the random demodulator requires just O(K log(W/K)) samples per second to stably reconstruct the signal.  ...  Thus, to achieve a tolerance of , we need only about terms.  ... 
doi:10.1109/tit.2009.2034811 fatcat:kf4rwgbycnf3bms4q6pz5dg33a

Differential Privacy in Practice

Hiep H. Nguyen, Jong Kim, Yoonho Kim
2013 Journal of Computing Science and Engineering  
We briefly review the problem of statistical disclosure control under differential privacy model, which entails a formal and ad omnia privacy guarantee separating the utility of the database and the risk  ...  Promises of differential privacy help to relieve concerns of privacy loss, which hinder the release of community-valuable data.  ...  ACKNOWLEDGMENTS This research was supported by World Class University program funded by the Ministry of Education, Science and Technology through the National Research Foundation of Korea (R31-10100).  ... 
doi:10.5626/jcse.2013.7.3.177 fatcat:xrcbyxpzfvh2tfdrr5572rdnku

Group Testing: An Information Theory Perspective

Matthew Aldridge, Oliver Johnson, Jonathan Scarlett
2019 Foundations and Trends in Communications and Information Theory  
If the preceding test is negative, A contains no defective items, and we halt. If the test is positive, continue. 3. If A consists of a single item, then that item is defective, and we halt.  ...  I(X 0,τ ; Y | X 1,τ ) (Equation (4.16)) ABOUT THIS SURVEY COUNTING BOUND AND RATE A REVIEW OF NOISELESS ADAPTIVE GROUP TESTING 2.  ...  Acknowledgments We are very grateful to Sidharth Jaggi, who made significant contributions to this project in its early stages and has provided helpful advice and feedback on its later drafts.  ... 
doi:10.1561/0100000099 fatcat:t3paagtzy5clnjo3t3ikdhwfpq

Cryptography in NC 0 [chapter]

Benny Applebaum
2014 Information Security and Cryptography  
We refer to this constant as the output locality of the function and denote by NC 0 c the class of NC 0 functions with locality c.  ...  We study the parallel time-complexity of basic cryptographic primitives such as one-way functions (OWFs) and pseudorandom generators (PRGs).  ...  We also thank Iftach Haitner and Emanuele Viola for enlightening us about old and new constructions of PRGs from OWFs and for sharing with us the results of [30] and [50] .  ... 
doi:10.1007/978-3-642-17367-7_4 fatcat:djfjlm7jtzcqbhjehw5td4zhjq

Cryptography in $NC^0$

Benny Applebaum, Yuval Ishai, Eyal Kushilevitz
2006 SIAM journal on computing (Print)  
We refer to this constant as the output locality of the function and denote by NC 0 c the class of NC 0 functions with locality c.  ...  We study the parallel time-complexity of basic cryptographic primitives such as one-way functions (OWFs) and pseudorandom generators (PRGs).  ...  We also thank Iftach Haitner and Emanuele Viola for enlightening us about old and new constructions of PRGs from OWFs and for sharing with us the results of [30] and [50] .  ... 
doi:10.1137/s0097539705446950 fatcat:kvyp5t75ifg7bnlw3ivmcdwuum
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