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检索条件"主题词=Streaming Algorithms"

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Online Sketching of Network Flows for Real-Time Stepping-Stone Detection

Online Sketching of Network Flows for Real-Time Stepping-Sto...

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25th Annual Computer Security Applications Conference

作者： Coskun, Baris Memon, Nasir NYU Polytech Inst Brooklyn NY 11201 USA

ISBN: (纸本)9780769539195

We present an efficient and robust stepping-stone detection scheme based on succinct packet-timing sketches of network flows. The proposed scheme employs an online algorithm to continuously maintain short sketches of flows from a stream of captured packets at the network boundary. These sketches are then used to identify pairs of network flows with similar packet-timing characteristics, which indicates potential stepping-stones. Succinct flow sketches enable the proposed scheme to compare a given pair of flows in constant time. In addition, flow sketches identify pairs of correlated flows from a given list of flows in sub-quadratic time, thereby allowing a more scalable solution as compared to known schemes. Finally, the proposed scheme is resistant to random delays and chaff, which are often employed by attackers to evade detection. To explore its efficacy, we mathematically analyze the robustness properties of the proposed flow sketch. We also experimentally measure the detection performance of the proposed scheme.

关键词： Network Security Stepping-Stones streaming algorithms Data Sketching

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AMS WITHOUT 4-WISE INDEPENDENCE ON PRODUCT DOMAINS

AMS WITHOUT 4-WISE INDEPENDENCE ON PRODUCT DOMAINS

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27th International Symposium on Theoretical Aspects of Computer Science (STACS)

作者： Braverman, Vladimir Chung, Kai-Min Liu, Zhenming Mitzenmacher, Michael Ostrovsky, Rafail Univ Calif Los Angeles Los Angeles CA 90024 USA Harvard Sch Engn & Appl Sci Cambridge MA USA

ISBN: (纸本)9783939897163

In their seminal work, Alon, Matias, and Szegedy introduced several sketching techniques, including showing that 4-wise independence is sufficient to obtain good approximations of the second frequency moment. In this work, we show that their sketching technique can be extended to product domains [n](k) by using the product of 4-wise independent functions on [n]. Our work extends that of Indyk and McGregor, who showed the result for k = 2. Their primary motivation was the problem of identifying correlations in data streams. In their model, a stream of pairs (i, j) 2 [n](2) arrive, giving a joint distribution (X, Y), and they find approximation algorithms for how close the joint distribution is to the product of the marginal distributions under various metrics, which naturally corresponds to how close X and Y are to being independent. By using our technique, we obtain a new result for the problem of approximating the l(2) distance between the joint distribution and the product of the marginal distributions for k-ary vectors, instead of just pairs, in a single pass. Our analysis gives a randomized algorithm that is a (1 +/- epsilon) approximation (with probability 1 - delta) that requires space logarithmic in n and m and proportional to 3(k).

关键词： Data Streams Randomized algorithms streaming algorithms Independence Sketches

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Volume and Irregularity Effects on Massively Multicore Packet Processors 18

Volume and Irregularity Effects on Massively Multicore Packe...

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18th Asia-Pacific Network Operations and Management Symposium (APNOMS)

作者： Zhanikeev, Marat Tokyo Univ Sci Sch Management Chiyoda Ku Fujimi 1-11-2 Tokyo 1020071 Japan

ISBN: (纸本)9784885523045

Irregularity is a recognized problem on many-and multi-core platforms but its effect remains to be studied. This paper focuses on multicore processors and assumes that packet traffic is processed by a large number of parallel jobs in realtime, while each job is implemented as a streaming algorithm. Analysis is performed using a real-life measurement dataset collected especially for this study while irregular traffic is modeled using a hotspot distribution. Results show that massively multicore processors are affected by both the total input volume and the irregularity.

关键词： massively multicore irregularity heterogeneity streaming data streaming algorithms packet traffic

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Linear Sketching over F₂ 33

Linear Sketching over F<sub>2</sub>

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33rd Computational Complexity Conference (CCC)

作者： Kannan, Sampath Mossel, Elchanan Sanyal, Swagato Yaroslavtsev, Grigory Univ Penn Philadelphia PA 19104 USA MIT Cambridge MA 02139 USA Nanyang Technol Univ Div Math Sci Singapore Singapore Natl Univ Singapore Ctr Quantum Technol Singapore Singapore Indiana Univ Bloomington IN USA

ISBN: (纸本)9783959770699

We initiate a systematic study of linear sketching over F-2. For a given Boolean function treated as f : F-2(n) -> F-2 a randomized F-2-sketch is a distribution M over d x n matrices with elements over F-2 such thatMx suffices for computing f(x) with high probability. Such sketches for d << n can be used to design small-space distributed and streaming algorithms. Motivated by these applications we study a connection between F-2-sketching and a two-player one-way communication game for the corresponding XOR-function. We conjecture that F-2-sketching is optimal for this communication game. Our results confirm this conjecture for multiple important classes of functions: 1) low-degree F-2-polynomials, 2) functions with sparse Fourier spectrum, 3) most symmetric functions, 4) recursive majority function. These results rely on a new structural theorem that shows that F-2-sketching is optimal (up to constant factors) for uniformly distributed inputs. Furthermore, we show that (non-uniform) streaming algorithms that have to process random updates over F-2 can be constructed as F-2-sketches for the uniform distribution. In contrast with the previous work of Li, Nguyen and Woodruff (STOC'14) who show an analogous result for linear sketches over integers in the adversarial setting our result does not require the stream length to be triply exponential in n and holds for streams of length (O) over tilde (n) constructed through uniformly random updates.

关键词： Linear sketch streaming algorithms XOR-functions Communication complexity

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A Real-time Algorithm for Finding Frequent Items Over Sliding Window 7

A Real-time Algorithm for Finding Frequent Items Over Slidin...

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7th IEEE International Conference on Software Engineering and Service Science (ICSESS)

作者： Li, Jing Liu, Jun Zhou, Wenli Beijing Univ Posts & Telecommun Beijing Key Lab Network Syst Architecure & Conver Beijing Peoples R China Beijing HaoHan Data Informat Technol Co LTD Beijing Peoples R China

ISBN: (纸本)9781467399043

The Paper presents an improved algorithm for finding frequent elements over a sliding window. It makes no assumption on the distribution of the input items' frequency. Its main structure composes of only a few maps and short queues. By using hash table and other data structure to manage counters, the running time is dramatically decreased. After thorough experiment and logical analysis, the running time has reduced to constant.

关键词： frequent items sliding window streaming algorithms network monitoring

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Approximability of all finite CSPs with linear sketches 62

Approximability of all finite CSPs with linear sketches

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62nd IEEE Annual Symposium on Foundations of Computer Science (FOCS)

作者： Chou, Chi-Ning Golovnev, Alexander Sudan, Madhu Velusamy, Santhoshini Harvard Univ John A Paulson Sch Engn & Appl Sci Boston MA 02115 USA Georgetown Univ Washington DC USA

ISBN: (纸本)9781665420556

A constraint satisfaction problem (CSP), Max-CSP(F), is specified by a finite set of constraints F subset of{[q](k) -> {0, 1}} for positive integers q and k. An instance of the problem on n variables is given by m applications of constraints from F to subsequences of the n variables, and the goal is to find an assignment to the variables that satisfies the maximum number of constraints. In the (gamma, beta)-approximation version of the problem, for parameters 0 <= beta < gamma <= 1, the goal is to distinguish instances where at least gamma fraction of the constraints can be satisfied from instances where at most beta fraction of the constraints can be satisfied. In this work we consider the approximability of this problem in the context of sketching algorithms and give a dichotomy result. Specifically, for every family F and every beta < gamma, we show that either a linear sketching algorithm solves the problem in polylogarithmic space, or the problem is not solvable by any sketching algorithm in o(root n) space. We also extend previously known lower bounds for general streaming algorithms to a wide variety of problems, and in particular the case of q = k = 2 where we get a dichotomy and the case when the satisfying assignments of f support a distribution on [q](k) with uniform marginals. Prior to this work, other than sporadic examples, the only systematic class of CSPs that were analyzed considered the setting of Boolean variables q = 2, binary constraints k = 2, singleton families vertical bar F vertical bar = 1 and only considered the setting where constraints are placed on literals rather than variables. Our positive results show wide applicability of bias-based algorithms used previously by [2] and [3], which we extend to include richer norm estimation algorithms, by giving a systematic way to discover biases. Our negative results combine the Fourier analytic methods of [4], which we extend to a wider class of CSPs, with a rich collection of reductions among c

关键词： streaming algorithms Approximation algorithms Constraint Satisfaction Linear Sketches

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Finding Heavy Distinct Hitters in Data Streams 11

Finding Heavy Distinct Hitters in Data Streams

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23rd Annual Symposium on Parallelism in algorithms and Architectures

作者： Locher, Thomas IBM Res Zurich Zurich Switzerland

ISBN: (纸本)9781450307437

A simple indicator for an anomaly in a network is a rapid increase in the total number of distinct network connections. While it is fairly easy to maintain an accurate estimate of the current total number of distinct connections using streaming algorithms that exhibit both a low space and computational complexity, identifying the network entities that are involved in the largest number of distinct connections efficiently is considerably harder. In this paper, we study the problem of finding all entities whose number of distinct (outgoing or incoming) network connections is at least a specific fraction of the total number of distinct connections. These entities are referred to as heavy distinct hitters. Since this problem is hard in general, we focus on randomized approximation techniques and propose a sampling-based and a sketch-based streaming algorithm. Both algorithms output a list of the potential heavy distinct hitters including the estimated counts of the corresponding number of distinct connections. We prove that, depending on the required level of accuracy of the output list, the space complexities of the presented algorithms are asymptotically optimal up to small logarithmic factors. Additionally, the algorithms are evaluated and compared using real network data in order to determine their usefulness in practice.

关键词： Network Monitoring Anomaly Detection streaming algorithms Heavy Distinct Hitter Space Complexity

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Submodular Optimization Over Sliding Windows 17

Submodular Optimization Over Sliding Windows

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26th International Conference on World Wide Web (WWW)

作者： Epasto, Alessandro Lattanzi, Silvio Vassilvitskii, Sergei Zadimoghaddam, Morteza Google New York NY 10011 USA

ISBN: (纸本)9781450349130

Maximizing submodular functions under cardinality constraints lies at the core of numerous data mining and machine learning applications, including data diversification, data summarization, and coverage problems. In this work, we study this question in the context of data streams, where elements arrive one at a time, and we want to design low-memory and fast update-time algorithms that maintain a good solution. Specifically, we focus on the sliding window model, where we are asked to maintain a solution that considers only the last W items. In this context, we provide the first non-trivial algorithm that maintains a provable approximation of the optimum using space sublinear in the size of the window. In particular we give a 1/3 - epsilon approximation algorithm that uses space polylogarithmic in the spread of the values of the elements, Phi, and linear in the solution size k for any constant epsilon > 0. At the same time, processing each element only requires a polylogarithmic number of evaluations of the function itself. When a better approximation is desired, we show a different algorithm that, at the cost of using more memory, provides a 1/2-epsilon approximation, and allows a tunable trade-off between average update time and space. This algorithm matches the best known approximation guarantees for submodular optimization in insertion-only streams, a less general formulation of the problem. We demonstrate the efficacy of the algorithms on a number of real world datasets, showing that their practical performance far exceeds the theoretical bounds. The algorithms preserve high quality solutions in streams with millions of items, while storing a negligible fraction of them.

关键词： submodular maximization sliding-window streams streaming algorithms

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Fast Hashing with Strong Concentration Bounds 2020

Fast Hashing with Strong Concentration Bounds

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52nd Annual ACM SIGACT Symposium on Theory of Computing (STOC)

作者： Aamand, Anders Knudsen, Jakob Baek Tejs Knudsen, Mathias Baek Tejs Rasmussen, Peter Michael Reichstein Thorup, Mikkel Univ Copenhagen BARC Copenhagen Denmark SupWiz Copenhagen Denmark

ISBN: (纸本)9781450369794

Previous work on tabulation hashing by Patrascu and Thorup from STOC'11 on simple tabulation and from SODA'13 on twisted tabulation offered Chernoff-style concentration bounds on hash based sums, e.g., the number of balls/keys hashing to a given bin, but under some quite severe restrictions on the expected values of these sums. The basic idea in tabulation hashing is to view a key as consisting of c = O(1) characters, e.g., a 64-bit key as c = 8 characters of 8-bits. The character domain Sigma should be small enough that character tables of size |Sigma| fit in fast cache. The schemes then use O(1) tables of this size, so the space of tabulation hashing is O(|Sigma|). However, the concentration bounds by Patrascu and Thorup only apply if the expected sums are << |Sigma|. To see the problem, consider the very simple case where we use tabulation hashing to throw n balls into m bins and want to analyse the number of balls in a given bin. With their concentration bounds, we are fine if n = m, for then the expected value is 1. However, if m = 2, as when tossing n unbiased coins, the expected value n/2 is >> |Sigma| for large data sets, e.g., data sets that do not fit in fast cache. To handle expectations that go beyond the limits of our small space, we need a much more advanced analysis of simple tabulation, plus a new tabulation technique that we call tabulation-permutation hashing which is at most twice as slow as simple tabulation. No other hashing scheme of comparable speed offers similar Chernoff-style concentration bounds.

关键词： hashing Chernoff bounds concentration bounds streaming algorithms sampling

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Advances in Incremental PCA algorithms 12th

Advances in Incremental PCA Algorithms

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12th International Conference on Parallel Processing and Applied Mathematics (PPAM)

作者： Halpern, Tal Toledo, Sivan Tel Aviv Univ Tel Aviv Israel

ISBN: (纸本)9783319780245;9783319780238

We present a range of new incremental (single-pass streaming) algorithms for incremental principal components analysis (IPCA) and show that they are more effective than exiting ones. IPCA algorithms process the columns of a matrix A one at a time and attempt to build a basis for a low-dimensional subspace that spans the dominant subspace of A. We present a unified framework for IPCA algorithms, show that many existing ones are parameterizations of it, propose new sophisticated algorithms, and show that both the new algorithms and many existing ones can be implemented more efficiently than was previously known. We also show that many existing algorithms can fail even in easy cases and we show experimentally that our new algorithms outperform existing ones.

关键词： Principal components analysis streaming algorithms Frequent directions

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