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Element Uniqueness Problem
In computational complexity theory, the element distinctness problem or element uniqueness problem is the problem of determining whether all the elements of a list are distinct. It is a well studied problem in many different models of computation. The problem may be solved by sorting the list and then checking if there are any consecutive equal elements; it may also be solved in linear expected time by a randomized algorithm that inserts each item into a hash table and compares only those elements that are placed in the same hash table cell. Several lower bounds in computational complexity are proved by reducing the element distinctness problem to the problem in question, i.e., by demonstrating that the solution of the element uniqueness problem may be quickly found after solving the problem in question. Decision tree complexity The number of comparisons needed to solve the problem of size n, in a comparison-based model of computation such as a decision tree or algebraic decision t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Complexity Theory
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying their computational complexity, i.e., the amount of resources needed to solve them, such as time and storage. Other measures of complexity are also used, such as the amount of communication (used in communication complexity), the number of gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). One of the roles of computationa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Randomized Complexity
A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random determined by the random bits; thus either the running time, or the output (or both) are random variables. One has to distinguish between algorithms that use the random input so that they always terminate with the correct answer, but where the expected running time is finite (Las Vegas algorithms, for example Quicksort), and algorithms which have a chance of producing an incorrect result (Monte Carlo algorithms, for example the Monte Carlo algorithm for the MFAS problem) or fail to produce a result either by signaling a failure or failing to terminate. In some cases, probabilistic algorithms are the only practical means of solving a problem. In common practice, randomized algor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decision Tree Model
In computational complexity the decision tree model is the model of computation in which an algorithm is considered to be basically a decision tree, i.e., a sequence of ''queries'' or ''tests'' that are done adaptively, so the outcome of the previous tests can influence the test is performed next. Typically, these tests have a small number of outcomes (such as a yes–no question) and can be performed quickly (say, with unit computational cost), so the worst-case time complexity of an algorithm in the decision tree model corresponds to the depth of the corresponding decision tree. This notion of computational complexity of a problem or an algorithm in the decision tree model is called its decision tree complexity or query complexity. Decision trees models are instrumental in establishing lower bounds for complexity theory for certain classes of computational problems and algorithms. Several variants of decision tree models have been introduced, depending on the computational mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Misra–Gries Heavy Hitters Algorithm
Misra and Gries defined the ''heavy-hitters problem'' (though they did not introduce the term ''heavy-hitters'') and described the first algorithm for it in the paper ''Finding repeated elements''. Their algorithm extends the Boyer-Moore majority finding algorithm in a significant way. One version of the heavy-hitters problem is as follows: Given is a bag of elements and an integer . Find the values that occur more than times in . The Misra-Gries algorithm solves the problem by making two passes over the values in , while storing at most values from and their number of occurrences during the course of the algorithm. Misra-Gries is one of the earliest streaming algorithms, and it is described below in those terms in section #Summaries. Misra–Gries algorithm A bag is a like a set in which the same value may occur multiple times. Assume that a bag is available as an array of elements. In the abstract description of the algorithm, we treat and its segments also as bags ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theory Of Computing
''Theory of Computing'' is a peer-reviewed open access scientific journal covering theoretical computer science. The journal was established in 2005 and is published by the Department of Computer Science of the University of Chicago. The editor-in-chief is László Babai László "Laci" Babai (born July 20, 1950, in Budapest) a fellow of the American Academy of Arts and Sciences, and won the Knuth Prize. Babai was an invited speaker at the International Congresses of Mathematicians in Kyoto (1990), Zürich (1994, ... (University of Chicago). External links * Publications established in 2005 Creative Commons Attribution-licensed journals Computer science journals University of Chicago {{compu-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symposium On Foundations Of Computer Science
The IEEE Annual Symposium on Foundations of Computer Science (FOCS) is an academic conference in the field of theoretical computer science. FOCS is sponsored by the IEEE Computer Society. As writes, FOCS and its annual Association for Computing Machinery counterpart STOC (the Symposium on Theory of Computing) are considered the two top conferences in theoretical computer science, considered broadly: they “are forums for some of the best work throughout theory of computing that promote breadth among theory of computing researchers and help to keep the community together.” includes regular attendance at FOCS and STOC as one of several defining characteristics of theoretical computer scientists. Awards The Knuth Prize for outstanding contributions to theoretical computer science is presented alternately at FOCS and STOC. Works of the highest quality presented at the conference are awarded the Best Paper Award. In addition, the Machtey Award is presented to the best student- ... [...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 |
Andris Ambainis
Andris Ambainis (born 18 January 1975) is a Latvian computer scientist active in the fields of quantum information theory and quantum computing. Education and career Ambainis has held past positions at the Institute for Advanced Study at Princeton, New Jersey and the Institute for Quantum Computing at the University of Waterloo. He is currently a professor in the Faculty of Computing at the University of Latvia. He received a Bachelors (1996), Masters (1997), and Doctorate (1997) in Computer Science from the University of Latvia, as well as a PhD (2001) from the University of California, Berkeley.Andris Ambainis' page at the . Contributions |
Quantum Algorithm
In quantum computing, a quantum algorithm is an algorithm which runs on a realistic model of quantum computation, the most commonly used model being the quantum circuit model of computation. A classical (or non-quantum) algorithm is a finite sequence of instructions, or a step-by-step procedure for solving a problem, where each step or instruction can be performed on a classical computer. Similarly, a quantum algorithm is a step-by-step procedure, where each of the steps can be performed on a quantum computer. Although all classical algorithms can also be performed on a quantum computer, the term quantum algorithm is usually used for those algorithms which seem inherently quantum, or use some essential feature of quantum computation such as quantum superposition or quantum entanglement. Problems which are undecidable using classical computers remain undecidable using quantum computers. What makes quantum algorithms interesting is that they might be able to solve some problems fa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expected Value
In probability theory, the expected value (also called expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a large number of independently selected outcomes of a random variable. The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by integration. In the axiomatic foundation for probability provided by measure theory, the expectation is given by Lebesgue integration. The expected value of a random variable is often denoted by , , or , with also often stylized as or \mathbb. History The idea of the expected value originated in the middle of the 17th century from the study of the so-called problem of points, which seeks to divide the stakes ''in a fair way'' between two players, who have to end th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sorting
Sorting refers to ordering data in an increasing or decreasing manner according to some linear relationship among the data items. # ordering: arranging items in a sequence ordered by some criterion; # categorizing: grouping items with similar properties. Ordering items is the combination of categorizing them based on equivalent order, and ordering the categories themselves. Sorting information or data In , arranging in an ordered sequence is called "sorting". Sorting is a common operation in many applications, and efficient algorithms to perform it have been developed. The most common uses of sorted sequences are: * making lookup or search efficient; * making merging of sequences efficient. * enable processing of data in a defined order. The opposite of sorting, rearranging a sequence of items in a random or meaningless order, is called shuffling. For sorting, either a weak order, "should not come after", can be specified, or a strict weak order, "should come before" (specif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
