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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 (link) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daniel Dominic Sleator
Daniel Dominic Kaplan Sleator (born 10 December 1953) is a Professor of Computer Science at Carnegie Mellon University, Pittsburgh, United States. In 1999, he won the ACM Paris Kanellakis Award (jointly with Robert Tarjan) for the splay tree data structure. He was one of the pioneers in amortized analysis of algorithms, early examples of which were the analyses of the move-to-front heuristic, and splay trees. He invented many data structures with Robert Tarjan, such as splay trees, link/cut trees, and skew heaps. The Sleator and Tarjan paper on the move-to-front heuristic first suggested the idea of comparing an online algorithm to an optimal offline algorithm, for which the term competitive analysis was later coined in a paper of Karlin, Manasse, Rudolph, and Sleator. Sleator also developed the theory of link grammars, and the Serioso music analyzer for analyzing meter and harmony in written music. Personal life Sleator was born to William Warner Sleator, Jr., a profes ... [...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 wo ... [...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 wi ...'' 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] |
Potential Method
In computational complexity theory, the potential method is a method used to analyze the amortized time and space complexity of a data structure, a measure of its performance over sequences of operations that smooths out the cost of infrequent but expensive operations.. Definition of amortized time In the potential method, a function Φ is chosen that maps states of the data structure to non-negative numbers. If ''S'' is a state of the data structure, Φ(''S'') represents work that has been accounted for ("paid for") in the amortized analysis but not yet performed. Thus, Φ(''S'') may be thought of as calculating the amount of potential energy stored in that state. The potential value prior to the operation of initializing a data structure is defined to be zero. Alternatively, Φ(''S'') may be thought of as representing the amount of disorder in state ''S'' or its distance from an ideal state. Let ''o'' be any individual operation within a sequence of operations on some data str ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dinic's Algorithm
Dinic's algorithm or Dinitz's algorithm is a strongly polynomial algorithm for computing the maximum flow in a flow network, conceived in 1970 by Israeli (formerly Soviet) computer scientist Yefim (Chaim) A. Dinitz. The algorithm runs in O(V^2 E) time and is similar to the Edmonds–Karp algorithm, which runs in O(VE^2) time, in that it uses shortest augmenting paths. The introduction of the concepts of the ''level graph'' and ''blocking flow'' enable Dinic's algorithm to achieve its performance. History Yefim Dinitz invented this algorithm in response to a pre-class exercise in Adelson-Velsky's algorithms class. At the time he was not aware of the basic facts regarding the Ford–Fulkerson algorithm. Dinitz mentions inventing his algorithm in January 1969, which was published in 1970 in the journal ''Doklady Akademii Nauk SSSR''. In 1974, Shimon Even and (his then Ph.D. student) Alon Itai at the Technion in Haifa were very curious and intrigued by Dinitz's algorithm as well as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Flow Problem
In optimization theory, maximum flow problems involve finding a feasible flow through a flow network that obtains the maximum possible flow rate. The maximum flow problem can be seen as a special case of more complex network flow problems, such as the circulation problem. The maximum value of an s-t flow (i.e., flow from source s to sink t) is equal to the minimum capacity of an s-t cut (i.e., cut severing s from t) in the network, as stated in the max-flow min-cut theorem. History The maximum flow problem was first formulated in 1954 by T. E. Harris and F. S. Ross as a simplified model of Soviet railway traffic flow. In 1955, Lester R. Ford, Jr. and Delbert R. Fulkerson created the first known algorithm, the Ford–Fulkerson algorithm.Ford, L.R., Jr.; Fulkerson, D.R., ''Flows in Networks'', Princeton University Press (1962). In their 1955 paper, Ford and Fulkerson wrote that the problem of Harris and Ross is formulated as follows (see p. 5):Consider a rail network conn ... [...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 nod ... [...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] |
Potential Method
In computational complexity theory, the potential method is a method used to analyze the amortized time and space complexity of a data structure, a measure of its performance over sequences of operations that smooths out the cost of infrequent but expensive operations.. Definition of amortized time In the potential method, a function Φ is chosen that maps states of the data structure to non-negative numbers. If ''S'' is a state of the data structure, Φ(''S'') represents work that has been accounted for ("paid for") in the amortized analysis but not yet performed. Thus, Φ(''S'') may be thought of as calculating the amount of potential energy stored in that state. The potential value prior to the operation of initializing a data structure is defined to be zero. Alternatively, Φ(''S'') may be thought of as representing the amount of disorder in state ''S'' or its distance from an ideal state. Let ''o'' be any individual operation within a sequence of operations on some data str ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
