Probability and Computing: Randomized Algorithms and Probabilistic Analysis

Buot, Max

doi:10.1198/jasa.2006.s74

Cited by 24 publications

(3 citation statements)

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“…Let be the number of distinct -mers stored in a dictionary D and let be the number of blocks in D. Under the assumption that the encoded -mers are independent from each other, the size of a block in D is at least with probability of at most . Applying Markov's inequality (Buot 2006), the probability that E is at least t is P…”

Section: Lower Neighborhood Queriesmentioning

confidence: 99%

Toward fast and accurate SNP genotyping from whole genome sequencing data for bedside diagnostics

Sun

Medvedev

2017

Preprint

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MotivationGenotyping a set of variants from a database is an important step for identifying known genetic traits and disease related variants within an individual. The growing size of variant databases as well as the high depth of sequencing data pose an efficiency challenge. In clinical applications, where time is crucial, alignment-based methods are often not fast enough. To fill the gap, Shajii et al. (2016) propose LAVA, an alignment-free genotyping method which is able to more quickly genotype SNPs; however, there remains large room for improvements in running time and accuracy.ResultsWe present the VarGeno method for SNP genotyping from lllumina whole genome sequencing data. VarGeno builds upon LAVA by improving the speed of k-mer querying as well as the accuracy of the genotyping strategy. We evaluate VarGeno on several read datasets using different genotyping SNP lists. VarGeno performs 7-13 times faster than LAVA with similar memory usage, while improving accuracy.AvailabilityVarGeno is freely available at: https://github.com/medvedevgroup/vargeno.

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Section: Lower Neighborhood Queriesmentioning

confidence: 99%

Toward fast and accurate SNP genotyping from whole genome sequencing data for bedside diagnostics

Sun

Medvedev

2017

Preprint

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“…Therefore, the independent object dominance assumption is invalid in uncertain preferences scenarios. 17 To the best of our knowledge, existing algorithms related to uncertain preferences are all sequential and adopt inclusion-exclusion principle 19 to express the skyline probability of an object. In general, it is very expensive for computing one single object's skyline probability, not even for all objects in the whole data set.…”

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confidence: 99%

Parallelization of skyline probability computation over uncertain preferences

Zhu

et al. 2017

Concurrency and Computation

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Summary Query processing over uncertain preferences is very common in real‐life situations, because many times, we cannot model users' preferences as strict partial orders. In this paper, we investigate skyline queries over uncertain preferences. The latest state‐of‐the‐art algorithm, called Usky‐base algorithm, makes significant advances. However, it still needs to be perfected in 2 aspects. (1) Theoretic analysis: The correctness of the algorithm is not fully verified. (2) Efficiency: Due to the heavy calculation introduced by adopting inclusion‐exclusion principle to express the skyline probability, it needs massive time when computing skyline probabilities for large data sets. To address the above 2 concerns, we first review the Usky‐base algorithm and lemmas it based on. Then we propose a novel parallel algorithm, called Parallel‐sky, to compute skyline probability of a given object. Moreover, we propose an adding algorithm and a deleting algorithm to deal with dynamic scenarios where new objects are added in and outdated objects are deleted out. Furthermore, we extend our algorithm from computing skyline probability of a given object to all objects in a data set. We conduct extensive experiments on real and synthetic data sets to validate the effectiveness and efficiency of our proposals.

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“…Lemma 6 The probability that Γ is bad is ≤ PROOF. We use the following version of the Chernoff bound as appears in [8]. Let X 1 , X 2 , .…”

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The Limits of Tractability in Resolution-Based Propositional Proof Systems

Dantchev

Martin

2010

Programs, Proofs, Processes

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Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractWe study classes of propositional contradictions based on the Least Number Principle (LNP) in the refutation system of Resolution and its generalisations with bounded conjunction, Res(k). We prove that any first-order sentence with no finite models that admits a Σ 1 interpretation of the LNP, relativised to a set that is quantifier-free definable, generates a sequence of propositional contradictions that have polynomially-sized refutations in the system Res(k), for some k. When one considers the LNP with total order we demonstrate that a Π 1 interpretation of this is sufficient to generate such a propositional sequence with polynomially-sized refutations in the system Res(k). On the other hand, we prove that a very simple first-order sentence that admits a Π 1 interpretation of the LNP (with partial and not total order) requires exponentially-sized refutations in Resolution.

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Probability and Computing: Randomized Algorithms and Probabilistic Analysis

Cited by 24 publications

References 0 publications

Toward fast and accurate SNP genotyping from whole genome sequencing data for bedside diagnostics

Toward fast and accurate SNP genotyping from whole genome sequencing data for bedside diagnostics

Parallelization of skyline probability computation over uncertain preferences

The Limits of Tractability in Resolution-Based Propositional Proof Systems

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