Contraction Hierarchies
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Contraction Hierarchies
In computer science, the method of contraction hierarchies is a speed-up technique for finding the shortest-path in a graph. The most intuitive applications are car-navigation systems: a user wants to drive from A to B using the quickest possible route. The metric optimized here is the travel time. Intersections are represented by vertices, the road sections connecting them by edges. The edge weights represent the time it takes to drive along this segment of the road. A path from A to B is a sequence of edges (road sections); the shortest path is the one with the minimal sum of edge weights among all possible paths. The shortest path in a graph can be computed using Dijkstra's algorithm but, given that road networks consist of tens of millions of vertices, this is impractical. Contraction hierarchies is a speed-up method optimized to exploit properties of graphs representing road networks. The speed-up is achieved by creating shortcuts in a preprocessing phase which are then used ...
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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 practical disciplines (including the design and implementation of hardware and software). Computer science is generally considered an area of 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 problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing security vulnerabilities. Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of repositories o ...
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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 compu ...
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Tree-depth
In graph theory, the tree-depth of a connected undirected graph G is a numerical invariant of G, the minimum height of a Trémaux tree for a supergraph of G. This invariant and its close relatives have gone under many different names in the literature, including vertex ranking number, ordered chromatic number, and minimum elimination tree height; it is also closely related to the cycle rank of directed graphs and the star height of regular languages. Intuitively, where the treewidth of a graph measures how far it is from being a tree, this parameter measures how far a graph is from being a star. Definitions The tree-depth of a graph G may be defined as the minimum height of a forest F with the property that every edge of G connects a pair of nodes that have an ancestor-descendant relationship to each other in F. If G is connected, this forest must be a single tree; it need not be a subgraph of G, but if it is, it is a Trémaux tree for G. The set of ancestor-descendant pairs ...
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Electric Vehicle
An electric vehicle (EV) is a vehicle that uses one or more electric motors for propulsion. It can be powered by a collector system, with electricity from extravehicular sources, or it can be powered autonomously by a battery (sometimes charged by solar panels, or by converting fuel to electricity using fuel cells or a generator). EVs include, but are not limited to, road and rail vehicles, surface and underwater vessels, electric aircraft and electric spacecraft. For road vehicles, together with other emerging automotive technologies such as autonomous driving, connected vehicles and shared mobility, EVs form a future mobility vision called Connected, Autonomous, Shared and Electric (CASE) Mobility. EVs first came into existence in the late 19th century, when electricity was among the preferred methods for motor vehicle propulsion, providing a level of comfort and ease of operation that could not be achieved by the gasoline cars of the time. Internal combustion en ...
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Cache (computing)
In computing, a cache ( ) is a hardware or software component that stores data so that future requests for that data can be served faster; the data stored in a cache might be the result of an earlier computation or a copy of data stored elsewhere. A ''cache hit'' occurs when the requested data can be found in a cache, while a ''cache miss'' occurs when it cannot. Cache hits are served by reading data from the cache, which is faster than recomputing a result or reading from a slower data store; thus, the more requests that can be served from the cache, the faster the system performs. To be cost-effective and to enable efficient use of data, caches must be relatively small. Nevertheless, caches have proven themselves in many areas of computing, because typical computer applications access data with a high degree of locality of reference. Such access patterns exhibit temporal locality, where data is requested that has been recently requested already, and spatial locality, where ...
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Parallel Computing
Parallel computing is a type of computation in which many calculations or processes are carried out simultaneously. Large problems can often be divided into smaller ones, which can then be solved at the same time. There are several different forms of parallel computing: bit-level, instruction-level, data, and task parallelism. Parallelism has long been employed in high-performance computing, but has gained broader interest due to the physical constraints preventing frequency scaling.S.V. Adve ''et al.'' (November 2008)"Parallel Computing Research at Illinois: The UPCRC Agenda" (PDF). Parallel@Illinois, University of Illinois at Urbana-Champaign. "The main techniques for these performance benefits—increased clock frequency and smarter but increasingly complex architectures—are now hitting the so-called power wall. The computer industry has accepted that future performance increases must largely come from increasing the number of processors (or cores) on a die, rather tha ...
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Geographical Distance
Geographical distance or geodetic distance is the distance measured along the surface of the earth. The formulae in this article calculate distances between points which are defined by geographical coordinates in terms of latitude and longitude. This distance is an element in solving the second (inverse) geodetic problem. Introduction Calculating the distance between geographical coordinates is based on some level of abstraction; it does not provide an ''exact'' distance, which is unattainable if one attempted to account for every irregularity in the surface of the earth. Common abstractions for the surface between two geographic points are: *Flat surface; *Spherical surface; *Ellipsoidal surface. All abstractions above ignore changes in elevation. Calculation of distances which account for changes in elevation relative to the idealized surface are not discussed in this article. Nomenclature Distance, D,\,\! is calculated between two points, P_1\,\! and P_2\,\!. The geograph ...
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Route Prediction
Route or routes may refer to: * Route (gridiron football), a path run by a wide receiver * route (command), a program used to configure the routing table * Route, County Antrim, an area in Northern Ireland * ''The Route'', a 2013 Ugandan film * Routes, Seine-Maritime, a commune in Seine-Maritime, France * ''Routes'' (video game), 2003 video game See also * Acronyms and abbreviations in avionics * Air route or airway * GPS route, a series of one or more GPS waypoints * Path (other) * Rout, a disorderly retreat of military units from the field of battle * Route number or road number * Router (other) * Router (woodworking) * Routing (other) * Routing table * Scenic route, a thoroughfare designated as scenic based on the scenery through which it passes * Trade route A trade route is a logistical network identified as a series of pathways and stoppages used for the commercial transport of cargo. The term can also be used to refer to trade over bodies o ...
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Traffic Simulation
Traffic simulation or the simulation of transportation systems is the mathematical modeling of transportation systems (e.g., freeway junctions, arterial routes, roundabouts, downtown grid systems, etc.) through the application of computer software to better help plan, design, and operate transportation systems. Simulation of transportation systems started over forty years ago, and is an important area of discipline in traffic engineering and transportation planning today. Various national and local transportation agencies, academic institutions and consulting firms use simulation to aid in their management of transportation networks. Simulation in transportation is important because it can study models too complicated for analytical or numerical treatment, can be used for experimental studies, can study detailed relations that might be lost in analytical or numerical treatment and can produce attractive visual demonstrations of present and future scenarios. To understand simulatio ...
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Global Positioning System
The Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of the global navigation satellite systems (GNSS) that provides geolocation and time information to a GPS receiver anywhere on or near the Earth where there is an unobstructed line of sight to four or more GPS satellites. It does not require the user to transmit any data, and operates independently of any telephonic or Internet reception, though these technologies can enhance the usefulness of the GPS positioning information. It provides critical positioning capabilities to military, civil, and commercial users around the world. Although the United States government created, controls and maintains the GPS system, it is freely accessible to anyone with a GPS receiver. The GPS project was started by the U.S. Department of Defense in 1973. The first prototype spacecraft was lau ...
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Search Space Of CH
Searching or search may refer to: Computing technology * Search algorithm, including keyword search ** :Search algorithms * Search and optimization for problem solving in artificial intelligence * Search engine technology, software for finding information ** Enterprise search, software or services for finding information within organizations ** Web search engine, a service for finding information on the World Wide Web Music * Search (band), a Malaysian rock band * "Searchin'", a 1957 song originally performed by The Coasters * "Searching" (China Black song), a 1991 song by China Black * "Searchin'" (CeCe Peniston song), a 1993 song by CeCe Peniston * "Searchin' (I Gotta Find a Man)", a 1983 dance song by Hazell Dean * "Searching" (INXS song), a 1997 song by INXS * "Searching" (Pete Rock & CL Smooth song), a 1995 song from the Pete Rock & CL Smooth album ''The Main Ingredient'' * ''Searching'', a 2013 album by Jay Diggins * "Searching", a 1980 single by Change * "Searchin ...
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Nested Dissection
In numerical analysis, nested dissection is a divide and conquer heuristic for the solution of sparse symmetric systems of linear equations based on graph partitioning. Nested dissection was introduced by ; the name was suggested by Garrett Birkhoff. Nested dissection consists of the following steps: *Form an undirected graph in which the vertices represent rows and columns of the system of linear equations, and an edge represents a nonzero entry in the sparse matrix representing the system. *Recursively partition the graph into subgraphs using separators, small subsets of vertices the removal of which allows the graph to be partitioned into subgraphs with at most a constant fraction of the number of vertices. *Perform Cholesky decomposition (a variant of Gaussian elimination for symmetric matrices), ordering the elimination of the variables by the recursive structure of the partition: each of the two subgraphs formed by removing the separator is eliminated first, and then the s ...
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