检索结果-内蒙古大学图书馆

Fast splitting algorithms for sparsity-constrained and noisy group testing

INFORMATION AND INFERENCE-A JOURNAL OF THE IMA 2023年第2期12卷 1141-1171页

作者： Price, Eric Scarlett, Jonathan Tan, Nelvin Univ Texas Austin Dept Comp Sci Austin TX 78712 USA Natl Univ Singapore Dept Comp Sci Singapore 117417 Singapore Natl Univ Singapore Dept Math Singapore 119076 Singapore Natl Univ Singapore Inst Data Sci Singapore 117602 Singapore Univ Cambridge Dept Engn Cambridge CB2 1PZ England

In group testing, the goal is to identify a subset of defective items within a larger set of items based on tests whose outcomes indicate whether at least one defective item is present. This problem is relevant in are... 详细信息

来源：评论

sublinear time algorithms

引用

SIAM JOURNAL ON DISCRETE MATHEMATICS 2011年第4期25卷 1562-1588页

作者： Rubinfeld, Ronitt Shapira, Asaf MIT Comp Sci Artificial Intelligence Lab Cambridge MA 02139 USA Tel Aviv Univ Blavatnik Sch Comp Sci Tel Aviv Israel Tel Aviv Univ Sch Math IL-69978 Tel Aviv Israel Georgia Inst Technol Sch Math & Comp Sci Atlanta GA 30332 USA

sublinear time algorithms represent a new paradigm in computing, where an algorithm must give some sort of an answer after inspecting only a very small portion of the input. We discuss the types of answers that one ca... 详细信息

来源：评论

On ultrametric 1-median selection

引用

THEORETICAL COMPUTER SCIENCE 2020年 828卷 65-69页

作者： Chang, Ching-Lueh Yuan Ze Univ Dept Comp Sci & Engn Taoyuan Taiwan

Consider the problem of finding a point in a finite ultrametric space with the minimum average distance to all points. We give this problem a Monte Carlo O ((log(2)(1/epsilon))/epsilon(3))-time (1 + epsilon)-approximation algorithm with success probability 1 - 0 (epsilon), for all epsilon > 0. (C) 2020 Elsevier B.V. All rights reserved.

关键词： 1-median selection sublinear time algorithms Ultrametric spaces Metric spaces Closeness centrality

来源：评论

学校读者我要写书评

暂无评论

Testing linear-invariant properties 61

Testing linear-invariant properties

引用

61st IEEE Annual Symposium on Foundations of Computer Science (FOCS)

作者： Tidor, Jonathan Zhao, Yufei MIT Dept Math Cambridge MA 02139 USA

ISBN: (纸本)9781728196213

Fix a prime p and a positive integer R. We study the property testing of functions F-p(n) -> [R]. We say that a property is testable if there exists an oblivious tester for this property with one-sided error and constant query complexity. Furthermore, a property is proximity oblivious-testable (PO-testable) if the test is also independent of the proximity parameter epsilon. It is known that a number of natural properties such as linearity and being a low degree polynomial are PO-testable. These properties are examples of linear-invariant properties, meaning that they are preserved under linear automorphisms of the domain. Following work of Kaufman and Sudan, the study of linear-invariant properties has been an important problem in arithmetic property testing. A central conjecture in this field, proposed by Bhattacharyya, Grigorescu, and Shapira, is that a linear-invariant property is testable if and only if it is semi subspace-hereditary. We prove two results, the first resolves this conjecture and the second classifies PO-testable properties. 1) A linear-invariant property is testable if and only if it is semi subspace-hereditary. 2) A linear-invariant property is PO-testable if and only if it is locally characterized. Our innovations are two-fold. We give a more powerful version of the compactness argument first introduced by Alon and Shapira. This relies on a new strong arithmetic regularity lemma in which one mixes different levels of Gowers uniformity. This allows us to extend the work of Bhattacharyya, Fischer, Hatami, Hatami, and Lovett by removing the bounded complexity restriction in their work. Our second innovation is a novel recoloring technique called patching. This Ramsey-theoretic technique is critical for working in the linear-invariant setting and allows us to remove the translation-invariant restriction present in previous work.

关键词： property testing sublinear time algorithms removal lemmas higher-order Fourier analysis

来源：评论

学校读者我要写书评

暂无评论

sublinear time ESTIMATION OF DEGREE DISTRIBUTION MOMENTS: THE ARBORICITY CONNECTION

引用

SIAM JOURNAL ON DISCRETE MATHEMATICS 2019年第4期33卷 2267-2285页

作者： Eden, Talya Ron, Dana Seshadhri, C. Tel Aviv Univ Sch Elect Engn IL-6948105 Tel Aviv Israel Univ Calif Santa Cruz Dept Comp Sci Santa Cruz CA 95064 USA

We revisit the classic problem of estimating the moments of the degree distribution of an undirected simple graph. Consider an undirected simple graph G = (V, E) with n (nonisolated) vertices, and define (for s > 0) M-s = Sigma(v is an element of V) d(v)(s). Our aim is to estimate M-s within a multiplicative error of (1 + epsilon) (for a given approximation parameter epsilon > 0) in sublinear time. We consider the sparse-graph model that allows access to uniform random vertices, queries for the degree of any vertex, and queries for a neighbor of any vertex. For the case of s = 1 (the average degree), O* (root n) queries suffice for any constant epsilon [U. Feige, SIAM J. Comput., 35 (2006), pp. 964-984], [O. Goldreich and D. Ron, Random Structures algorithms, 32 (2008), pp. 473-493]. (We use the O* notation to suppress dependencies in log n and 1/epsilon.) Gonen, Ron, and Shavitt [SIAM J. Discrete Math., 25 (2011), pp. 1365-1411] extended this result to all integral s > 0 by designing an algorithm that performs O* (n(1-1/(s+1))) queries. (Strictly speaking, their algorithm approximates the number of star-subgraphs of a given size, but a slight modification gives an algorithm for moments.) We design a new, significantly simpler algorithm for this problem. In the worst case, it exactly matches the bounds of Gonen, Ron, and Shavitt and has a much simpler proof. More importantly, the running time of this algorithm is connected to the arboricity of G. This is (essentially) the maximum density of an induced subgraph. For the family of graphs with arboricity at most alpha, it has a query complexity of O* (***(1/s) M-s(1/s) + min {m/M-s(1/s), m.n(s-1)/M-s) which is always upper bounded by O* (n alpha/M-s(1/s)). Thus, for the class of constant-arboricity graphs (which includes, among others, all minor-closed families and preferential attachment graphs), we can estimate the average degree in O* (1) queries, and we can estimate the variance of the degree distribution in O*

关键词： sublinear time algorithms degeneracy degree distribution approximation algorithms arboricity degree moments

来源：评论

学校读者我要写书评

暂无评论

Local Computation algorithms 19

Local Computation Algorithms

引用

38th ACM Symposium on Principles of Distributed Computing (PODC)

作者： Rubinfeld, Ronitt MIT 77 Massachusetts Ave Cambridge MA 02139 USA Tel Aviv Univ Tel Aviv Israel

ISBN: (纸本)9781450362177

Consider a setting in which inputs to and outputs from a computational problem are so large, that there is not time to read them in their entirety. However, if one is only interested in small parts of the output at any given time, is it really necessary to solve the entire computational problem? Is it even necessary to view the whole input? We survey recent work in the model of "local computation algorithms" which for a given input, supports queries by a user to values of specified bits of a legal output. The goal is to design local computation algorithms in such a way that very little of the input needs to be seen in order to determine the value of any single bit of the output. Though this model describes sequential computations, techniques from local distributed algorithms have been extremely important in designing efficient local computation algorithms. In this talk, we describe results on a variety of problems for which sublinear time and space local computation algorithms have been developed - we will give special focus to finding maximal independent sets and sparse spanning graphs.

关键词： sublinear time algorithms randomized algorithms approximation algorithms

来源：评论

学校读者我要写书评

暂无评论

sublinear time Low-Rank Approximation of Positive Semidefinite Matrices 58

Sublinear Time Low-Rank Approximation of Positive Semidefini...

引用

58th IEEE Annual Symposium on Foundations of Computer Science (FOCS)

作者： Musco, Cameron Woodruff, David P. MIT 77 Massachusetts Ave Cambridge MA 02139 USA Carnegie Mellon Univ Pittsburgh PA 15213 USA

ISBN: (纸本)9781538634646

We show how to compute a relative-error low-rank approximation to any positive semidefinite (PSD) matrix in sublinear time, i.e., for any n x n PSD matrix A, in (O) over tilde (n . poly(k/epsilon)) time we output a rank-k matrix B, in factored form, for which parallel to A - B parallel to(2)(F) <= (1 + c) parallel to A - A(k)parallel to(2)(F), where A(k) is the best rank-k approximation to A. When k and 1/epsilon are not too large compared to the sparsity of A, our algorithm does not need to read all entries of the matrix. Hence, we significantly improve upon previous nnz(A) time algorithms based on oblivious subspace embeddings, and bypass an nnz(A) time lower bound for general matrices (where nnz(A) denotes the number of non-zero entries in the matrix). We prove time lower bounds for low-rank approximation of PSD matrices, showing that our algorithm is close to optimal. Finally, we extend our techniques to give sublinear time algorithms for low-rank approximation of A in the (often stronger) spectral norm metric parallel to A - B parallel to(2)(2) and for ridge regression on PSD matrices.

关键词： low-rank approximation leverage score sampling sublinear time algorithms matrix sketching

来源：评论

学校读者我要写书评

暂无评论

An Adaptive sublinear-time Block Sparse Fourier Transform 2017

An Adaptive Sublinear-Time Block Sparse Fourier Transform

引用

49th Annual ACM-SIGACT Symposium on Theory of Computing (STOC)

作者： Cevher, Volkan Kapralov, Michael Scarlett, Jonathan Zandieh, Amir Ecole Polytech Fed Lausanne Lausanne Switzerland

ISBN: (纸本)9781450345286

The problem of approximately computing the k dominant Fourier coeficients of a vector X quickly, and using few samples in time domain, is known as the Sparse Fourier Transform (sparse FFT) problem. A long line of work on the sparse FFT has resulted in algorithms with O(k logn log(n/k)) runtime [Hassanieh et al., STOC' 12] and O(k logn) sample complexity [Indyk et al., FOCS' 14]. This paper revisits the sparse FFT problem with the added twist that the sparse coeficients approximately obey a (k(0), k(1))-block sparse model. In this model, signal frequencies are clustered in k(0) intervals with width k(1) in Fourier space, and k = k(0)k(1) is the total sparsity. Our main result is the first sparse FFT algorithm for (k(0);k(1))-block sparse signals with a sample complexity of O*(k(0)k(1) + k(0) log(1 + k(0)) log n) at constant signal-to-noise ratios, and sublinear runtime. Our algorithm crucially uses adaptivity to achieve the improved sample complexity bound, and we provide a lower bound showing that this is essential in the Fourier setting: Any non-adaptive algorithm must use Omega(k(0)k(1) log n/k(0) k(1)) samples for the (k(0);k(1))-block sparse model, ruling out improvements over the vanilla sparsity assumption. Our main technical innovation for adaptivity is a new randomized energy-based importance sampling technique that may be of independent interest.

关键词： Sparse Fourier transform sublinear time algorithms adaptive sampling energy-based importance sampling lower bounds

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法