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Minimum Bottleneck Spanning Tree
In mathematics, a minimum bottleneck spanning tree (MBST) in an undirected graph is a spanning tree in which the most expensive edge is as cheap as possible. A bottleneck edge is the highest weighted edge in a spanning tree. A spanning tree is a minimum bottleneck spanning tree if the graph does not contain a spanning tree with a smaller bottleneck edge weight. For a directed graph, a similar problem is known as Minimum Bottleneck Spanning Arborescence (MBSA). Definitions Undirected graphs In an undirected graph and a function , let be the set of all spanning trees ''T''''i''. Let ''B''(''T''''i'') be the maximum weight edge for any spanning tree ''T''''i''. We define subset of minimum bottleneck spanning trees ''S''′ such that for every and we have for all ''i'' and ''k''. The graph on the right is an example of MBST, the red edges in the graph form a MBST of . Directed graphs An arborescence of graph ''G'' is a directed tree of ''G'' which contains a dire ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spanning Tree
In the mathematical field of graph theory, a spanning tree ''T'' of an undirected graph ''G'' is a subgraph that is a tree which includes all of the vertices of ''G''. In general, a graph may have several spanning trees, but a graph that is not connected will not contain a spanning tree (see about spanning forests below). If all of the edges of ''G'' are also edges of a spanning tree ''T'' of ''G'', then ''G'' is a tree and is identical to ''T'' (that is, a tree has a unique spanning tree and it is itself). Applications Several pathfinding algorithms, including Dijkstra's algorithm and the A* search algorithm, internally build a spanning tree as an intermediate step in solving the problem. In order to minimize the cost of power networks, wiring connections, piping, automatic speech recognition, etc., people often use algorithms that gradually build a spanning tree (or many such trees) as intermediate steps in the process of finding the minimum spanning tree. The Internet and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MBSA Example 6
Microsoft Baseline Security Analyzer (MBSA) is a discontinued software tool which is no longer available from Microsoft that determines security state by assessing missing security updates and less-secure security settings within Microsoft Windows, Windows components such as Internet Explorer, IIS web server, and products Microsoft SQL Server, and Microsoft Office macro settings. Security updates are determined by the current version of MBSA using the Windows Update Agent present on Windows computers since Windows 2000 Service Pack 3. The less-secure settings, often called Vulnerability Assessment (VA) checks, are assessed based on a hard-coded set of registry and file checks. An example of a VA might be that permissions for one of the directories in the /www/root folder of IIS could be set at too low a level, allowing unwanted modification of files from outsiders. Version history Versions 1.2.1 and below run on NT4, Windows 2000, Windows XP, and Windows Server 2003, provide su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci Heap
In computer science, a Fibonacci heap is a data structure for priority queue operations, consisting of a collection of heap-ordered trees. It has a better amortized running time than many other priority queue data structures including the binary heap and binomial heap. Michael L. Fredman and Robert E. Tarjan developed Fibonacci heaps in 1984 and published them in a scientific journal in 1987. Fibonacci heaps are named after the Fibonacci numbers, which are used in their running time analysis. For the Fibonacci heap, the find-minimum operation takes constant ('' O''(1)) amortized time. The insert and decrease key operations also work in constant amortized time. Deleting an element (most often used in the special case of deleting the minimum element) works in ''O''(log ''n'') amortized time, where ''n'' is the size of the heap. This means that starting from an empty data structure, any sequence of ''a'' insert and decrease key operations and ''b'' delete operations would take ''O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dijkstra's Algorithm
Dijkstra's algorithm ( ) is an algorithm for finding the shortest paths between nodes in a graph, which may represent, for example, road networks. It was conceived by computer scientist Edsger W. Dijkstra in 1956 and published three years later. The algorithm exists in many variants. Dijkstra's original algorithm found the shortest path between two given nodes, but a more common variant fixes a single node as the "source" node and finds shortest paths from the source to all other nodes in the graph, producing a shortest-path tree. For a given source node in the graph, the algorithm finds the shortest path between that node and every other. It can also be used for finding the shortest paths from a single node to a single destination node by stopping the algorithm once the shortest path to the destination node has been determined. For example, if the nodes of the graph represent cities and edge path costs represent driving distances between pairs of cities connected by a dir ... [...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] |
Harold N
Harold may refer to: People * Harold (given name), including a list of persons and fictional characters with the name * Harold (surname), surname in the English language * András Arató, known in meme culture as "Hide the Pain Harold" Arts and entertainment * Harold (film), ''Harold'' (film), a 2008 comedy film * ''Harold'', an 1876 poem by Alfred, Lord Tennyson * ''Harold, the Last of the Saxons'', an 1848 book by Edward Bulwer-Lytton, 1st Baron Lytton * ''Harold or the Norman Conquest'', an opera by Frederic Cowen * ''Harold'', an 1885 opera by Eduard Nápravník * Harold, a character from the cartoon List of The Grim Adventures of Billy & Mandy characters#Harold, ''The Grim Adventures of Billy & Mandy'' *Harold & Kumar, a US movie; Harold/Harry is the main actor in the show. Places ;In the United States * Alpine, Los Angeles County, California, an erstwhile settlement that was also known as Harold * Harold, Florida, an unincorporated community * Harold, Kentucky, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MBSA Example 11
Microsoft Baseline Security Analyzer (MBSA) is a discontinued software tool which is no longer available from Microsoft that determines security state by assessing missing security updates and less-secure security settings within Microsoft Windows, Windows components such as Internet Explorer, IIS web server, and products Microsoft SQL Server, and Microsoft Office macro settings. Security updates are determined by the current version of MBSA using the Windows Update Agent present on Windows computers since Windows 2000 Service Pack 3. The less-secure settings, often called Vulnerability Assessment (VA) checks, are assessed based on a hard-coded set of registry and file checks. An example of a VA might be that permissions for one of the directories in the /www/root folder of IIS could be set at too low a level, allowing unwanted modification of files from outsiders. Version history Versions 1.2.1 and below run on NT4, Windows 2000, Windows XP, and Windows Server 2003, provide su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MBSA Example 10
Microsoft Baseline Security Analyzer (MBSA) is a discontinued software tool which is no longer available from Microsoft that determines security state by assessing missing security updates and less-secure security settings within Microsoft Windows, Windows components such as Internet Explorer, IIS web server, and products Microsoft SQL Server, and Microsoft Office macro settings. Security updates are determined by the current version of MBSA using the Windows Update Agent present on Windows computers since Windows 2000 Service Pack 3. The less-secure settings, often called Vulnerability Assessment (VA) checks, are assessed based on a hard-coded set of registry and file checks. An example of a VA might be that permissions for one of the directories in the /www/root folder of IIS could be set at too low a level, allowing unwanted modification of files from outsiders. Version history Versions 1.2.1 and below run on NT4, Windows 2000, Windows XP, and Windows Server 2003, provide su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
