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Shortest Path Problems
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. The problem of finding the shortest path between two intersections on a road map may be modeled as a special case of the shortest path problem in graphs, where the vertices correspond to intersections and the edges correspond to road segments, each weighted by the length of the segment. Definition The shortest path problem can be defined for graphs whether undirected, directed, or mixed. It is defined here for undirected graphs; for directed graphs the definition of path requires that consecutive vertices be connected by an appropriate directed edge. Two vertices are adjacent when they are both incident to a common edge. A path in an undirected graph is a sequence of vertices P = ( v_1, v_2, \ldots, v_n ) \in V \times V \times \cdots \times V such that v_i is adjacent to v_ for 1 \leq i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Complexity
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] |
Computer Network
A computer network is a set of computers sharing resources located on or provided by network nodes. The computers use common communication protocols over digital interconnections to communicate with each other. These interconnections are made up of telecommunication network technologies, based on physically wired, optical, and wireless radio-frequency methods that may be arranged in a variety of network topologies. The nodes of a computer network can include personal computers, servers, networking hardware, or other specialised or general-purpose hosts. They are identified by network addresses, and may have hostnames. Hostnames serve as memorable labels for the nodes, rarely changed after initial assignment. Network addresses serve for locating and identifying the nodes by communication protocols such as the Internet Protocol. Computer networks may be classified by many criteria, including the transmission medium used to carry signals, bandwidth, communications pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rubik's Cube
The Rubik's Cube is a Three-dimensional space, 3-D combination puzzle originally invented in 1974 by Hungarians, Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, the puzzle was licensed by Rubik to be sold by Pentangle Puzzles in the UK in 1978, and then by Ideal Toy Company, Ideal Toy Corp in 1980 via businessman Tibor Laczi and Seven Towns founder Tom Kremer. The cube was released internationally in 1980 and became one of the most recognized icons in popular culture. It won the 1980 Spiel des Jahres, German Game of the Year special award for Best Puzzle. , 350 million cubes had been sold worldwide, making it the world's bestselling puzzle game and bestselling toy. The Rubik's Cube was inducted into the US National Toy Hall of Fame in 2014. On the original classic Rubik's Cube, each of the six faces was covered by nine stickers, each of one of six solid colours: white, red, blue, orange, green, and yellow. Some later versions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Machine
An abstract machine is a computer science theoretical model that allows for a detailed and precise analysis of how a computer system functions. It is analogous to a mathematical function in that it receives inputs and produces outputs based on predefined rules. Abstract machines vary from literal machines in that they are expected to perform correctly and independently of hardware. Abstract machines are “machines” because they allow step-by-step execution of programmes; they are “ abstract” because they ignore many aspects of actual ( hardware) machines. A typical abstract machine consists of a definition in terms of input, output, and the set of allowable operations used to turn the former into the latter. They can be used for purely theoretical reasons as well as models for real-world computer systems. In the theory of computation, abstract machines are often used in thought experiments regarding computability or to analyse the complexity of algorithms. This use of abstr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Google Maps
Google Maps is a web mapping platform and consumer application offered by Google. It offers satellite imagery, aerial photography, street maps, 360° interactive panoramic views of streets ( Street View), real-time traffic conditions, and route planning for traveling by foot, car, bike, air (in beta) and public transportation. , Google Maps was being used by over 1 billion people every month around the world. Google Maps began as a C++ desktop program developed by brothers Lars and Jens Rasmussen at Where 2 Technologies. In October 2004, the company was acquired by Google, which converted it into a web application. After additional acquisitions of a geospatial data visualization company and a real-time traffic analyzer, Google Maps was launched in February 2005. The service's front end utilizes JavaScript, XML, and Ajax. Google Maps offers an API that allows maps to be embedded on third-party websites, and offers a locator for businesses and other organizations in numero ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MapQuest
MapQuest (stylized as mapquest) is an American free online web mapping service. It was launched in 1996 as the first commercial web mapping service. MapQuest vies for market share with competitors such as Google Maps and Here. History MapQuest's origins date to 1967 with the founding of Cartographic Services, a division of R.R. Donnelley & Sons in Chicago, Illinois, which moved to Lancaster, Pennsylvania, in 1969. In the mid-1980s, R.R. Donnelley & Sons began generating maps and routes for customers, with cooperation by Barry Glick, a University at Buffalo Ph.D. In 1994 it was spun off as GeoSystems Global Corporation. Much of the code was adapted for use on the Internet to create the MapQuest web service in 1996. MapQuest's original services were mapping (referred to as "Interactive Atlas") and driving directions (called "TripQuest"). Sensing the emerging demand for spatial applications on the Internet, and with crippling network latency in Lancaster, the executive team of Barr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Web Mapping
Web mapping or an online mapping is the process of using maps, usually created through geographic information systems (GIS), on the Internet, more specifically in the World Wide Web (WWW). A web map or an online map is both served and consumed, thus web mapping is more than just web cartography, it is a service by which consumers may choose what the map will show. Web GIS emphasizes geodata processing aspects more involved with design aspects such as data acquisition and server software architecture such as data storage and algorithms, than it does the end-user reports themselves. The terms ''web GIS'' and ''web mapping ''remain somewhat synonymous. Web GIS uses web maps, and end users who are ''web mapping'' are gaining analytical capabilities. The term ''location-based services'' refers to ''web mapping'' consumer goods and services. Web mapping usually involves a web browser or other user agent capable of client-server interactions. Questions of quality, usability, social ben ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Seidel's Algorithm
Seidel's algorithm is an algorithm designed by Raimund Seidel in 1992 for the all-pairs-shortest-path problem for undirected, unweighted, connected graphs. It solves the problem in O(V^\omega \log V) expected time for a graph with V vertices, where \omega 2 and O(V^2 \log^2 V) for \omega = 2. Computing the shortest-paths lengths The Python code below assumes the input graph is given as a n\times n 0-1 adjacency matrix In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. In the special case of a finite simp ... A with zeros on the diagonal. It defines the function APD which returns a matrix with entries D_ such that D_ is the length of the shortest path between the vertices i and j. The matrix class used can be any matrix class implementation supporting the multiplication, exponentiation, and indexing operators (for examp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gabow's Algorithm (single-source Shortest Paths)
Gabow's algorithm may refer to any of several algorithms by Harold N. Gabow, including: * Path-based strong component algorithm In graph theory, the strongly connected components of a directed graph may be found using an algorithm that uses depth-first search in combination with two stacks, one to keep track of the vertices in the current component and the second to keep tr ... * Gabow's algorithm (single-source shortest paths) {{Disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bucket Queue
A bucket queue is a data structure that implements the priority queue abstract data type: it maintains a dynamic collection of elements with numerical priorities and allows quick access to the element with minimum (or maximum) priority. In the bucket queue, the priorities must be integers, and it is particularly suited to applications in which the priorities have a small range. A bucket queue has the form of an array of buckets: an array data structure, indexed by the priorities, whose cells contain collections of items with the same priority as each other. With this data structure, insertion of elements and changes of their priority take constant time. Searching for and removing the minimum-priority element takes time proportional to the number of buckets or, by maintaining a pointer to the most recently found bucket, in time proportional to the difference in priorities between successive operations. The bucket queue is the priority-queue analogue of pigeonhole sort (also calle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Sorting
In computer science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge ''uv'' from vertex ''u'' to vertex ''v'', ''u'' comes before ''v'' in the ordering. For instance, the vertices of the graph may represent tasks to be performed, and the edges may represent constraints that one task must be performed before another; in this application, a topological ordering is just a valid sequence for the tasks. Precisely, a topological sort is a graph traversal in which each node ''v'' is visited only after all its dependencies are visited''.'' A topological ordering is possible if and only if the graph has no directed cycles, that is, if it is a directed acyclic graph (DAG). Any DAG has at least one topological ordering, and algorithms are known for constructing a topological ordering of any DAG in linear time. Topological sorting has many applications especially in ranking problems such as feedback arc set. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
