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K-independent Hashing
In computer science, a family of hash functions is said to be ''k''-independent, ''k''-wise independent or ''k''-universal if selecting a function at random from the family guarantees that the hash codes of any designated ''k'' keys are independent random variables (see precise mathematical definitions below). Such families allow good average case performance in randomized algorithms or data structures, even if the input data is chosen by an adversary. The trade-offs between the degree of independence and the efficiency of evaluating the hash function are well studied, and many ''k''-independent families have been proposed. Background The goal of hashing is usually to map keys from some large domain (universe) U into a smaller range, such as m bins (labelled = \). In the analysis of randomized algorithms and data structures, it is often desirable for the hash codes of various keys to "behave randomly". For instance, if the hash code of each key were an independent random choi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical disciplines (including the design and implementation of Computer architecture, hardware and Computer programming, software). Computer science is generally considered an area of research, academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing Vulnerability (computing), security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Progr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SIAM Journal On Computing
The ''SIAM Journal on Computing'' is a scientific journal focusing on the mathematical and formal aspects of computer science. It is published by the Society for Industrial and Applied Mathematics (SIAM). Although its official ISO abbreviation is ''SIAM J. Comput.'', its publisher and contributors frequently use the shorter abbreviation ''SICOMP''. SICOMP typically hosts the special issues of the IEEE Annual Symposium on Foundations of Computer Science (FOCS) and the Annual ACM Symposium on Theory of Computing (STOC), where about 15% of papers published in FOCS and STOC each year are invited to these special issues. For example, Volume 48 contains 11 out of 85 papers published in FOCS 2016. References * External linksSIAM Journal on Computing on |
MinHash
In computer science and data mining, MinHash (or the min-wise independent permutations locality sensitive hashing scheme) is a technique for quickly estimating how similar two sets are. The scheme was invented by , and initially used in the AltaVista search engine to detect duplicate web pages and eliminate them from search results.. It has also been applied in large-scale clustering problems, such as clustering documents by the similarity of their sets of words.. Jaccard similarity and minimum hash values The Jaccard similarity coefficient is a commonly used indicator of the similarity between two sets. Let be a set and and be subsets of , then the Jaccard index is defined to be the ratio of the number of elements of their intersection and the number of elements of their union: : J(A,B) = . This value is 0 when the two sets are disjoint, 1 when they are equal, and strictly between 0 and 1 otherwise. Two sets are more similar (i.e. have relatively more members in common) wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karloff–Zwick Algorithm
The Karloff–Zwick algorithm, in computational complexity theory, is a randomised approximation algorithm taking an instance of MAX-3SAT Boolean satisfiability problem as input. If the instance is satisfiable, then the expected weight of the assignment found is at least 7/8 of optimal. There is strong evidence (but not a mathematical proof) that the algorithm achieves 7/8 of optimal even on unsatisfiable MAX-3SAT instances. Howard Karloff and Uri Zwick presented the algorithm in 1997.. The algorithm is based on semidefinite programming. It can be derandomized using, e.g., the techniques from to yield a deterministic polynomial-time algorithm with the same approximation guarantees. Comparison to random assignment For the related MAX-E3SAT problem, in which all clauses in the input 3SAT formula are guaranteed to have exactly three literals, the simple randomized approximation algorithm which assigns a truth value to each variable independently and uniformly at random satisfi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimensionality Reduction
Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its intrinsic dimension. Working in high-dimensional spaces can be undesirable for many reasons; raw data are often sparse as a consequence of the curse of dimensionality, and analyzing the data is usually computationally intractable (hard to control or deal with). Dimensionality reduction is common in fields that deal with large numbers of observations and/or large numbers of variables, such as signal processing, speech recognition, neuroinformatics, and bioinformatics. Methods are commonly divided into linear and nonlinear approaches. Approaches can also be divided into feature selection and feature extraction. Dimensionality reduction can be used for noise reduction, data visualization, cluster analysis, or as an intermediat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Count Sketch
Count sketch is a type of dimensionality reduction that is particularly efficient in statistics, machine learning and algorithms. It was invented by Moses Charikar, Kevin Chen and Martin Farach-Colton in an effort to speed up the AMS Sketch by Alon, Matias and Szegedy for approximating the frequency moments of streams. The sketch is nearly identical to the Feature hashing algorithm by John Moody, but differs in its use of hash functions with low dependence, which makes it more practical. In order to still have a high probability of success, the median trick is used to aggregate multiple count sketches, rather than the mean. These properties allow use for explicit kernel methods, bilinear pooling in neural networks and is a cornerstone in many numerical linear algebra algorithms.Woodruff, David P. "Sketching as a Tool for Numerical Linear Algebra." Theoretical Computer Science 10.1-2 (2014): 1–157. Mathematical definition 1. For constants w and t (to be defined later) ind ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flajolet–Martin Algorithm
The Flajolet–Martin algorithm is an algorithm for approximating the number of distinct elements in a stream with a single pass and space-consumption logarithmic in the maximal number of possible distinct elements in the stream (the count-distinct problem). The algorithm was introduced by Philippe Flajolet and G. Nigel Martin in their 1984 article "Probabilistic Counting Algorithms for Data Base Applications". Later it has been refined in "LogLog counting of large cardinalities" by Marianne Durand and Philippe Flajolet, and "HyperLogLog: The analysis of a near-optimal cardinality estimation algorithm" by Philippe Flajolet et al. In their 2010 article "An optimal algorithm for the distinct elements problem", Daniel M. Kane, Jelani Nelson and David P. Woodruff give an improved algorithm, which uses nearly optimal space and has optimal ''O''(1) update and reporting times. The algorithm Assume that we are given a hash function \mathrm(x) that maps input x to integers in the range ; ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jelani Nelson
Jelani Osei Nelson ( am, ጄላኒ ኔልሰን; born June 28, 1984) is an Ethiopian-American Professor of Electrical Engineering and Computer Sciences at the University of California, Berkeley. He won the 2014 Presidential Early Career Award for Scientists and Engineers. Nelson is the creator of ''AddisCoder'', a computer science summer program for Ethiopian high school students in Addis Ababa. Early life and education Nelson was born to an Ethiopian mother and an African-American father in Los Angeles, then grew up in St. Thomas, U.S. Virgin Islands. He studied mathematics and computer science at the Massachusetts Institute of Technology and remained there to complete his doctoral studies in computer science. His Master's dissertation, ''External-Memory Search Trees with Fast Insertions'', was supervised by Bradley C. Kuszmaul and Charles E. Leiserson. He was a member of the theory of computation group, working on efficient algorithms for massive datasets. His doctoral dissert ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daniel Kane (mathematician)
Daniel Mertz Kane (born 1986) is an American mathematician. He is an associate professor with a joint position in the Mathematics Department and the Computer Science and Engineering Department at the University of California, San Diego.. Early life and education Kane was born in Madison, Wisconsin, to Janet E. Mertz and Jonathan M. Kane, professors of oncology and of mathematics and computer science, respectively... The article is primarily about a study jointly authored by Kane's parents, but also mentions Kane's IMO results. He attended Wingra School, a small alternative K-8 school in Madison that focuses on self-guided education. By 3rd grade, he had mastered K through 9th-grade mathematics. Starting at age 13, he took honors math courses at the University of Wisconsin–Madison and did research under the mentorship of Ken Ono while dual enrolled at Madison West High School. He earned gold medals in the 2002 and 2003 International Mathematical Olympiads. Prior to his 17th b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cuckoo Hashing
Cuckoo hashing is a scheme in computer programming for resolving hash collisions of values of hash functions in a table, with worst-case constant lookup time. The name derives from the behavior of some species of cuckoo, where the cuckoo chick pushes the other eggs or young out of the nest when it hatches in a variation of the behavior referred to as brood parasitism; analogously, inserting a new key into a cuckoo hashing table may push an older key to a different location in the table. History Cuckoo hashing was first described by Rasmus Pagh and Flemming Friche Rodler in a 2001 conference paper. The paper was awarded the European Symposium on Algorithms Test-of-Time award in 2020. Operations Cuckoo hashing is a form of open addressing in which each non-empty cell of a hash table contains a key or key–value pair. A hash function is used to determine the location for each key, and its presence in the table (or the value associated with it) can be found by examining that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lecture Notes In Computer Science
''Lecture Notes in Computer Science'' is a series of computer science books published by Springer Science+Business Media since 1973. Overview The series contains proceedings, post-proceedings, monographs, and Festschrifts. In addition, tutorials, state-of-the-art surveys, and "hot topics" are increasingly being included. The series is indexed by DBLP. See also *''Monographiae Biologicae'', another monograph series published by Springer Science+Business Media *''Lecture Notes in Physics'' *''Lecture Notes in Mathematics'' *''Electronic Workshops in Computing ''Electronic Workshops in Computing'' (eWiC) is a publication series by the British Computer Society. The series provides free online access for conferences and workshops in the area of computing. For example, the EVA London Conference proceeding ...'', published by the British Computer Society References External links * Publications established in 1973 Computer science books Series of non-fiction books Springer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
