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Top Tree
A top tree is a data structure based on a binary tree for unrooted dynamic trees that is used mainly for various path-related operations. It allows simple divide-and-conquer algorithms. It has since been augmented to maintain dynamically various properties of a tree such as diameter, center and median. A top tree \Re is defined for an ''underlying tree'' \mathcal and a set \partial of at most two vertices called as External Boundary Vertices Glossary Boundary Node See Boundary Vertex Boundary Vertex A vertex in a connected subtree is a ''Boundary Vertex'' if it is connected to a vertex outside the subtree by an edge. External Boundary Vertices Up to a pair of vertices in the top tree \Re can be called as External Boundary Vertices, they can be thought of as Boundary Vertices of the cluster which represents the entire top tree. Cluster A ''cluster'' is a connected subtree with at most two Boundary Vertices. The set of Boundary Vertices of a given cluster \mathcal is deno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Structure
In computer science, a data structure is a data organization, management, and storage format that is usually chosen for Efficiency, efficient Data access, access to data. More precisely, a data structure is a collection of data values, the relationships among them, and the functions or operations that can be applied to the data, i.e., it is an algebraic structure about data. Usage Data structures serve as the basis for abstract data types (ADT). The ADT defines the logical form of the data type. The data structure implements the physical form of the data type. Different types of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks. For example, Relational database, relational databases commonly use B-tree indexes for data retrieval, while compiler Implementation, implementations usually use hash tables to look up identifiers. Data structures provide a means to manage large amounts of data efficiently for uses such a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mikkel Thorup
Mikkel Thorup (born 1965) is a Danish computer scientist working at University of Copenhagen. He completed his undergraduate education at Technical University of Denmark and his doctoral studies at Oxford University in 1993. From 1993 to 1998, he was at University of Copenhagen and from 1998 to 2013 he was at AT&T Labs-Research in New Jersey. Since 2013 he has been at the University of Copenhagen as a Professor and Head of Center for Efficient Algorithms and Data Structures (EADS). Thorup's main work is in algorithms and data structures. One of his best-known results is a linear-time algorithm for the single-source shortest paths problem in undirected graphs (Thorup, 1999). With Mihai Pătraşcu he has shown that simple tabulation hashing schemes achieve the same or similar performance criteria as hash families that have higher independence in worst case, while permitting speedier implementations. Thorup has been editor of the area algorithm and data structures for Jou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomas H
Thomas may refer to: People * List of people with given name Thomas * Thomas (name) * Thomas (surname) * Saint Thomas (other) * Thomas Aquinas (1225–1274) Italian Dominican friar, philosopher, and Doctor of the Church * Thomas the Apostle * Thomas (bishop of the East Angles) (fl. 640s–650s), medieval Bishop of the East Angles * Thomas (Archdeacon of Barnstaple) (fl. 1203), Archdeacon of Barnstaple * Thomas, Count of Perche (1195–1217), Count of Perche * Thomas (bishop of Finland) (1248), first known Bishop of Finland * Thomas, Earl of Mar (1330–1377), 14th-century Earl, Aberdeen, Scotland Geography Places in the United States * Thomas, Illinois * Thomas, Indiana * Thomas, Oklahoma * Thomas, Oregon * Thomas, South Dakota * Thomas, Virginia * Thomas, Washington * Thomas, West Virginia * Thomas County (other) * Thomas Township (other) Elsewhere * Thomas Glacier (Greenland) Arts, entertainment, and media * ''Thomas'' (Burton ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Art Of Computer Programming
''The Art of Computer Programming'' (''TAOCP'') is a comprehensive monograph written by the computer scientist Donald Knuth presenting programming algorithms and their analysis. Volumes 1–5 are intended to represent the central core of computer programming for sequential machines. When Knuth began the project in 1962, he originally conceived of it as a single book with twelve chapters. The first three volumes of what was then expected to be a seven-volume set were published in 1968, 1969, and 1973. Work began in earnest on Volume 4 in 1973, but was suspended in 1977 for work on typesetting prompted by the second edition of Volume 2. Writing of the final copy of Volume 4A began in longhand in 2001, and the first online pre-fascicle, 2A, appeared later in 2001. The first published installment of Volume 4 appeared in paperback as Fascicle 2 in 2005. The hardback Volume 4A, combining Volume 4, Fascicles 0–4, was published in 2011. Volume 4, Fascicle 6 ("Satisfiability") was r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Donald Knuth
Donald Ervin Knuth ( ; born January 10, 1938) is an American computer scientist, mathematician, and professor emeritus at Stanford University. He is the 1974 recipient of the ACM Turing Award, informally considered the Nobel Prize of computer science. Knuth has been called the "father of the analysis of algorithms". He is the author of the multi-volume work '' The Art of Computer Programming'' and contributed to the development of the rigorous analysis of the computational complexity of algorithms and systematized formal mathematical techniques for it. In the process, he also popularized the asymptotic notation. In addition to fundamental contributions in several branches of theoretical computer science, Knuth is the creator of the TeX computer typesetting system, the related METAFONT font definition language and rendering system, and the Computer Modern family of typefaces. As a writer and scholar, Knuth created the WEB and CWEB computer programming systems designed to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamic Connectivity
In computing and graph theory, a dynamic connectivity structure is a data structure that dynamically maintains information about the connected components of a graph. The set ''V'' of vertices of the graph is fixed, but the set ''E'' of edges can change. The three cases, in order of difficulty, are: * Edges are only added to the graph (this can be called ''incremental connectivity''); * Edges are only deleted from the graph (this can be called ''decremental connectivity''); * Edges can be either added or deleted (this can be called ''fully dynamic connectivity''). After each addition/deletion of an edge, the dynamic connectivity structure should adapt itself such that it can give quick answers to queries of the form "is there a path between ''x'' and ''y''?" (equivalently: "do vertices ''x'' and ''y'' belong to the same connected component?"). Incremental connectivity If edges can only be added, then the dynamic connectivity problem can be solved by a Disjoint-set data structure. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamic Algorithm
Dynamic problems in computational complexity theory are problems stated in terms of the changing input data. In the most general form a problem in this category is usually stated as follows: * Given a class of input objects, find efficient algorithms and data structures to answer a certain query about a set of input objects each time the input data is modified, i.e., objects are inserted or deleted. Problems of this class have the following measures of complexity: * Space the amount of memory space required to store the data structure; * Initialization time time required for the initial construction of the data structure; * Insertion time time required for the update of the data structure when one more input element is added; * Deletion time time required for the update of the data structure when an input element is deleted; * Query time time required to answer a query; * Other operations specific to the problem in question The overall set of computations for a dynamic problem i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler Tour Tree
The Euler tour technique (ETT), named after Leonhard Euler, is a method in graph theory for representing trees. The tree is viewed as a directed graph that contains two directed edges for each edge in the tree. The tree can then be represented as a Eulerian circuit of the directed graph, known as the Euler tour representation (ETR) of the tree. The ETT allows for efficient, parallel computation of solutions to common problems in algorithmic graph theory. It was introduced by Tarjan and Vishkin in 1984. Construction Given an undirected tree presented as a set of edges, the Euler tour representation (ETR) can be constructed in parallel as follows: * We construct a symmetric list of directed edges: ** For each undirected edge in the tree, insert (''u'',''v'') and (''v'',''u'') in the edge list. * Sort the edge list lexicographically. (Here we assume that the nodes of the tree are ordered, and that the root is the first element in this order.) * Construct adjacency lists for each n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Link/cut Tree
A link/cut tree is a data structure for representing a forest, a set of rooted trees, and offers the following operations: * Add a tree consisting of a single node to the forest. * Given a node in one of the trees, disconnect it (and its subtree) from the tree of which it is part. * Attach a node to another node as its child. * Given a node, find the root of the tree to which it belongs. By doing this operation on two distinct nodes, one can check whether they belong to the same tree. The represented forest may consist of very deep trees, so if we represent the forest as a plain collection of parent pointer trees, it might take us a long time to find the root of a given node. However, if we represent each tree in the forest as a link/cut tree, we can find which tree an element belongs to in O(log(n)) amortized amortized time. Moreover, we can quickly adjust the collection of link/cut trees to changes in the represented forest. In particular, we can adjust it to merge (lin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Persistent Data Structure
In computing, a persistent data structure or not ephemeral data structure is a data structure that always preserves the previous version of itself when it is modified. Such data structures are effectively immutable, as their operations do not (visibly) update the structure in-place, but instead always yield a new updated structure. The term was introduced in Driscoll, Sarnak, Sleator, and Tarjans' 1986 article. A data structure is partially persistent if all versions can be accessed but only the newest version can be modified. The data structure is fully persistent if every version can be both accessed and modified. If there is also a meld or merge operation that can create a new version from two previous versions, the data structure is called confluently persistent. Structures that are not persistent are called ''ephemeral''. These types of data structures are particularly common in logical and functional programming, as languages in those paradigms discourage (or fully forbi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Link/cut Tree
A link/cut tree is a data structure for representing a forest, a set of rooted trees, and offers the following operations: * Add a tree consisting of a single node to the forest. * Given a node in one of the trees, disconnect it (and its subtree) from the tree of which it is part. * Attach a node to another node as its child. * Given a node, find the root of the tree to which it belongs. By doing this operation on two distinct nodes, one can check whether they belong to the same tree. The represented forest may consist of very deep trees, so if we represent the forest as a plain collection of parent pointer trees, it might take us a long time to find the root of a given node. However, if we represent each tree in the forest as a link/cut tree, we can find which tree an element belongs to in O(log(n)) amortized amortized time. Moreover, we can quickly adjust the collection of link/cut trees to changes in the represented forest. In particular, we can adjust it to merge (lin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
