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Tarjan's Off-line Least Common Ancestors Algorithm
In computer science, Tarjan's off-line lowest common ancestors algorithm is an algorithm for computing lowest common ancestors for pairs of nodes in a tree, based on the union-find data structure. The lowest common ancestor of two nodes ''d'' and ''e'' in a rooted tree ''T'' is the node ''g'' that is an ancestor of both ''d'' and ''e'' and that has the greatest depth in ''T''. It is named after Robert Tarjan, who discovered the technique in 1979. Tarjan's algorithm is an offline algorithm; that is, unlike other lowest common ancestor algorithms, it requires that all pairs of nodes for which the lowest common ancestor is desired must be specified in advance. The simplest version of the algorithm uses the union-find data structure, which unlike other lowest common ancestor data structures can take more than constant time per operation when the number of pairs of nodes is similar in magnitude to the number of nodes. A later refinement by speeds the algorithm up to linear time In c ... [...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] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a Heuristic (computer science), heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lowest Common Ancestor
In graph theory and computer science, the lowest common ancestor (LCA) (also called least common ancestor) of two nodes and in a Tree (graph theory), tree or directed acyclic graph (DAG) is the lowest (i.e. deepest) node that has both and as descendants, where we define each node to be a descendant of itself (so if has a direct connection from , is the lowest common ancestor). The LCA of and in is the shared ancestor of and that is located farthest from the root. Computation of lowest common ancestors may be useful, for instance, as part of a procedure for determining the distance between pairs of nodes in a tree: the distance from to can be computed as the distance from the root to , plus the distance from the root to , minus twice the distance from the root to their lowest common ancestor . In ontology (information science), ontologies, the lowest common ancestor is also known as the least common ancestor. In a tree data structure where each node points to its pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Union-find
In computer science, a disjoint-set data structure, also called a union–find data structure or merge–find set, is a data structure that stores a collection of disjoint (non-overlapping) sets. Equivalently, it stores a partition of a set into disjoint subsets. It provides operations for adding new sets, merging sets (replacing them by their union), and finding a representative member of a set. The last operation makes it possible to find out efficiently if any two elements are in the same or different sets. While there are several ways of implementing disjoint-set data structures, in practice they are often identified with a particular implementation called a disjoint-set forest. This is a specialized type of forest which performs unions and finds in near-constant amortized time. To perform a sequence of addition, union, or find operations on a disjoint-set forest with nodes requires total time , where is the extremely slow-growing inverse Ackermann function. Disj ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rooted Tree
In graph theory, a tree is an undirected graph in which any two vertices are connected by ''exactly one'' path, or equivalently a connected acyclic undirected graph. A forest is an undirected graph in which any two vertices are connected by ''at most one'' path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees. A polytreeSee . (or directed tree or oriented treeSee .See . or singly connected networkSee .) is a directed acyclic graph (DAG) whose underlying undirected graph is a tree. A polyforest (or directed forest or oriented forest) is a directed acyclic graph whose underlying undirected graph is a forest. The various kinds of data structures referred to as trees in computer science have underlying graphs that are trees in graph theory, although such data structures are generally rooted trees. A rooted tree may be directed, called a directed rooted tree, either making all its edges point away from the root—in which case it is called an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Tarjan
Robert Endre Tarjan (born April 30, 1948) is an American computer scientist and mathematician. He is the discoverer of several graph algorithms, including Tarjan's off-line lowest common ancestors algorithm, and co-inventor of both splay trees and Fibonacci heaps. Tarjan is currently the James S. McDonnell Distinguished University Professor of Computer Science at Princeton University, and the Chief Scientist at Intertrust Technologies Corporation. Early life and education He was born in Pomona, California. His father, raised in Hungary, was a child psychiatrist, specializing in mental retardation, and ran a state hospital. As a child, Tarjan read a lot of science fiction, and wanted to be an astronomer. He became interested in mathematics after reading Martin Gardner's mathematical games column in Scientific American. He became seriously interested in math in the eighth grade, thanks to a "very stimulating" teacher. While he was in high school, Tarjan got a job, where he work ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Time
In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor. Since an algorithm's running time may vary among different inputs of the same size, one commonly considers the worst-case time complexity, which is the maximum amount of time required for inputs of a given size. Less common, and usually specified explicitly, is the average-case complexity, which is the average of the time taken on inputs of a given size (this makes sense because there are only a finite number of possible inputs of a given size). In both cases, the time complexity is generally expresse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Disjoint-set Data Structure
In computer science, a disjoint-set data structure, also called a union–find data structure or merge–find set, is a data structure that stores a collection of disjoint (non-overlapping) sets. Equivalently, it stores a partition of a set into disjoint subsets. It provides operations for adding new sets, merging sets (replacing them by their union), and finding a representative member of a set. The last operation makes it possible to find out efficiently if any two elements are in the same or different sets. While there are several ways of implementing disjoint-set data structures, in practice they are often identified with a particular implementation called a disjoint-set forest. This is a specialized type of forest which performs unions and finds in near-constant amortized time. To perform a sequence of addition, union, or find operations on a disjoint-set forest with nodes requires total time , where is the extremely slow-growing inverse Ackermann function. Disjo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of The ACM
The ''Journal of the ACM'' is a peer-reviewed scientific journal covering computer science in general, especially theoretical aspects. It is an official journal of the Association for Computing Machinery. Its current editor-in-chief is Venkatesan Guruswami. The journal was established in 1954 and "computer scientists universally hold the ''Journal of the ACM'' in high esteem". See also * ''Communications of the ACM ''Communications of the ACM'' is the monthly journal of the Association for Computing Machinery (ACM). It was established in 1958, with Saul Rosen as its first managing editor. It is sent to all ACM members. Articles are intended for readers with ...'' References External links * Publications established in 1954 Computer science journals Association for Computing Machinery academic journals Bimonthly journals English-language journals {{compu-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Algorithms
The following is a list of well-known algorithms along with one-line descriptions for each. Automated planning Combinatorial algorithms General combinatorial algorithms * Brent's algorithm: finds a cycle in function value iterations using only two iterators * Floyd's cycle-finding algorithm: finds a cycle in function value iterations * Gale–Shapley algorithm: solves the stable marriage problem * Pseudorandom number generators (uniformly distributed—see also List of pseudorandom number generators for other PRNGs with varying degrees of convergence and varying statistical quality): ** ACORN generator ** Blum Blum Shub ** Lagged Fibonacci generator ** Linear congruential generator ** Mersenne Twister Graph algorithms * Coloring algorithm: Graph coloring algorithm. * Hopcroft–Karp algorithm: convert a bipartite graph to a maximum cardinality matching * Hungarian algorithm: algorithm for finding a perfect matching * Prüfer coding: conversion between a labeled tree an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
