Counting by Coin Tossings

Flajolet, Philippe

doi:10.1007/978-3-540-30502-6_1

Cited by 20 publications

(13 citation statements)

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“…The problem of counting items in a large datastream inspires several classes of algorithms, including approximate counting, probabilistic counting, sampling, and sketches; see "Counting by Coin Tossings" [7] for a survey. Approximate counting is beneficial by itself, and lately it has been combined with the other classes.…”

Section: Approximate Counting In Streamsmentioning

confidence: 99%

Flexible approximate counting

Mitchell

Day

2011

Proceedings of the 15th Symposium on International Database Engineering &Amp; Applications - IDEAS '11

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Approximate counting [18] is useful for data stream and database summarization. It can help in many settings that allow only one pass over the data, want low memory usage, and can accept some relative error. Approximate counters use fewer bits; we focus on 8-bits but our results are general. These small counters represent a sparse sequence of larger numbers. Counters are incremented probabilistically based on the spacing between the numbers they represent. Our contributions are a customized distribution of counter values and efficient strategies for deciding when to increment them.At run-time, users may independently select the spacing (accuracy) of the approximate counter for small, medium, and large values. We allow the user to select the maximum number to count up to, and our algorithm will select the exponential base of the spacing. These provide additional flexibility over both classic and Csűrös's [4] floating-point approximate counting. These provide additional structure, a useful schema for users, over Kruskal and Greenberg [13].We describe two new and efficient strategies for incrementing approximate counters: use a deterministic countdown or sample from a geometric distribution. In Csűrös all increments are powers of two, so random bits rather than full random numbers can be used. We also provide the option to use powers-of-two but retain flexibility. We show when each strategy is fastest in our implementation.

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Section: Approximate Counting In Streamsmentioning

confidence: 99%

Flexible approximate counting

Mitchell

Day

2011

Proceedings of the 15th Symposium on International Database Engineering &Amp; Applications - IDEAS '11

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“…Exponential functionals of Poisson process and, more generally, of Lévy processes, appear in a number of important applications. For instance, they are relevant to the analysis of randomized algorithms (F lajolet , 2004) and in mathematical finance (B ertoin and Y or , 2005). In D umas et al.…”

Section: Related Research Areasmentioning

confidence: 99%

A survey on performance analysis of warehouse carousel systems

Litvak

Vlasiou

2010

Statistica Neerlandica

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This paper gives an overview of recent research on the performance evaluation and design of carousel systems. We discuss picking strategies for problems involving one carousel, consider the throughput of the system for problems involving two carousels, give an overview of related problems in this area, and present an extensive literature review. Emphasis has been given on future research directions in this area.Comment: 42 pages, 6 figures, 128 references, invited pape

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“…The relative standard deviation of the estimaten is shown in [10] to be very nearly independent of n. Kruskal and Greenberg presented an adaptable approach to approximate counting based on the Morris algorithm in their work [8]. A review of probabilistic counting algorithms for data streaming applications can be found in [4].…”

Section: Background and Related Workmentioning

confidence: 99%

“…We pause at this point to recall that if fn satisfies the recursion of the type fn+1 = gn + fn (4) for n ≥ k, then a closed form expression for fn valid for all n ≥ k + 1 can be obtained via (3) is of type (4). Assuming that the counter starts at x0 = const, the initial condition of (3) is y0 = f (x0) = const (that is, for k = 0), and the solution is…”

Section: Algorithm Descriptionmentioning

confidence: 99%

An algorithm for approximate counting using limited memory resources

CvetkovskiAndrej¹

2007

SIGMETRICS Perform. Eval. Rev.

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This paper describes a randomized algorithm for approximate counting that preserves the same modest memory requirements of log(log n) bits per counter as the approximate counting algorithm introduced in the seminal paper of R. Morris (1978), and in addition, is characterized by (i) lower expected number of memory accesses and (ii) lower standard error on more than 99 percent of its counting range. An exact analysis of the relevant statistical properties of the algorithm is carried out. Performance evaluation via simulations is also provided to validate the presented theory.Given its properties, the presented algorithm is suitable as a basic building block of data streaming applications having a large number of simultaneous counters and/or operating at very high speeds. As such, it is applicable to a wide range of measurement and monitoring operations, including performance monitoring of communication hardware, measurements for optimization in large database systems, and gathering statistics for data compression.

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Counting by Coin Tossings

Cited by 20 publications

References 20 publications

Flexible approximate counting

Flexible approximate counting

A survey on performance analysis of warehouse carousel systems

An algorithm for approximate counting using limited memory resources

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