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Transport Network
A transport network, or transportation network, is a network or graph in geographic space, describing an infrastructure that permits and constrains movement or flow. Examples include but are not limited to road networks, railways, air routes, pipelines, aqueducts, and power lines. The digital representation of these networks, and the methods for their analysis, is a core part of spatial analysis, geographic information systems, public utilities, and transport engineering. Network analysis is an application of the theories and algorithms of graph theory and is a form of proximity analysis. History The applicability of graph theory to geographic phenomena was recognized at an early date. Many of the early problems and theories undertaken by graph theorists were inspired by geographic situations, such as the Seven Bridges of Königsberg problem, which was one of the original foundations of graph theory when it was solved by Leonhard Euler in 1736. In the 1970s, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spatial Network
A spatial network (sometimes also geometric graph) is a graph in which the vertices or edges are ''spatial elements'' associated with geometric objects, i.e., the nodes are located in a space equipped with a certain metric.M. Barthelemy, "Morphogenesis of Spatial Networks", Springer (2018). The simplest mathematical realization of spatial network is a lattice or a random geometric graph (see figure in the right), where nodes are distributed uniformly at random over a two-dimensional plane; a pair of nodes are connected if the Euclidean distance is smaller than a given neighborhood radius. Transportation and mobility networks, Internet, mobile phone networks, power grids, social and contact networks and biological neural networks are all examples where the underlying space is relevant and where the graph's topology alone does not contain all the information. Characterizing and understanding the structure, resilience and the evolution of spatial networks is crucial for ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Friction Of Distance
Friction of distance is a core principle of geography that states that movement incurs some form of cost, in the form of physical effort, energy, time, and/or the expenditure of other resources, and that these costs are proportional to the distance traveled. This cost is thus a resistance against movement, analogous (but not directly related) to the effect of friction against movement in classical mechanics. The subsequent preference for minimizing distance and its cost underlies a vast array of geographic patterns from economic agglomeration to wildlife migration, as well as many of the theories and techniques of spatial analysis, such as Tobler's first law of geography, network routing, and cost distance analysis. To a large degree, friction of distance is the primary reason why geography is relevant to many aspects of the world, although its importance (and perhaps the importance of geography) has been decreasing with the development of transportation and communication techno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lloyd's Algorithm
In electrical engineering and computer science, Lloyd's algorithm, also known as Voronoi iteration or relaxation, is an algorithm named after Stuart P. Lloyd for finding evenly spaced sets of points in subsets of Euclidean spaces and partitions of these subsets into well-shaped and uniformly sized convex cells. Like the closely related ''k''-means clustering algorithm, it repeatedly finds the centroid of each set in the partition and then re-partitions the input according to which of these centroids is closest. In this setting, the mean operation is an integral over a region of space, and the nearest centroid operation results in Voronoi diagrams. Although the algorithm may be applied most directly to the Euclidean plane, similar algorithms may also be applied to higher-dimensional spaces or to spaces with other non-Euclidean metrics. Lloyd's algorithm can be used to construct close approximations to centroidal Voronoi tessellations of the input, which can be used for quantiza ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polynomial Time
In theoretical 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 gener ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chinese Postman Problem
In graph theory and combinatorial optimization, Guan's route problem, the Chinese postman problem, postman tour or route inspection problem is to find a shortest closed path or circuit that visits every edge of an (connected) undirected graph at least once. When the graph has an Eulerian circuit (a closed walk that covers every edge once), that circuit is an optimal solution. Otherwise, the optimization problem is to find the smallest number of graph edges to duplicate (or the subset of edges with the minimum possible total weight) so that the resulting multigraph does have an Eulerian circuit. It can be solved in polynomial time, unlike the Travelling salesman problem, Travelling Salesman Problem which is NP-hardness, NP-hard. It is different from the Travelling Salesman Problem in that the travelling salesman cannot repeat visited nodes and does not have to visit every edge. The problem was originally studied by the Chinese mathematician Meigu Guan in 1960, whose Chinese paper w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Route Inspection
Route or routes may refer to: * Air route, route structure or airway * GPS route, a series of one or more GPS waypoints * 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 * Routes, Seine-Maritime, a commune in Seine-Maritime, France * ''Routes'', a 2003 video game by Leaf See also * Acronyms and abbreviations in avionics * 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) * The Route (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 la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vehicle Routing Problem
The vehicle routing problem (VRP) is a combinatorial optimization and integer programming problem which asks "What is the optimal set of routes for a fleet of vehicles to traverse in order to deliver to a given set of customers?" It generalises the travelling salesman problem (TSP). It first appeared in a paper by George Dantzig and John Ramser in 1959, in which the first algorithmic approach was written and was applied to petrol deliveries. Often, the context is that of delivering goods located at a central depot to customers who have placed orders for such goods. The objective of the VRP is to minimize the total route cost. In 1964, Clarke and Wright improved on Dantzig and Ramser's approach using an effective greedy algorithm called the savings algorithm. Determining the optimal solution to VRP is NP-hard, so the size of problems that can be optimally solved using mathematical programming or combinatorial optimization can be limited. Therefore, commercial solvers tend to use H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Traveling Salesman Problem
In the theory of computational complexity, the travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research. The travelling purchaser problem, the vehicle routing problem and the ring star problem are three generalizations of TSP. The decision version of the TSP (where given a length ''L'', the task is to decide whether the graph has a tour whose length is at most ''L'') belongs to the class of NP-complete problems. Thus, it is possible that the worst-case running time for any algorithm for the TSP increases superpolynomially (but no more than exponentially) with the number of cities. The problem was first formulated in 1930 and is one of the most intensively studied problems ... [...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 weighted graph, which may represent, for example, a road network. It was conceived by computer scientist Edsger W. Dijkstra in 1956 and published three years later. Dijkstra's algorithm finds the shortest path from a given source node to every other node. It can be used to find the shortest path to a specific destination node, by terminating the algorithm after determining the shortest path to the destination node. For example, if the nodes of the graph represent cities, and the costs of edges represent the distances between pairs of cities connected by a direct road, then Dijkstra's algorithm can be used to find the shortest route between one city and all other cities. A common application of shortest path algorithms is network routing protocols, most notably IS-IS (Intermediate System to Intermediate System) and OSPF (Open Shortest Path First). It is also employed as a subroutine in ... [...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 panorama, interactive panoramic views of streets (Google Street View, Street View), real-time traffic conditions, and route planner, route planning for traveling by foot, car, bike, air (in Software release life cycle#Beta, beta) and public transportation. , Google Maps was being used by over one billion people every month around the world. Google Maps began as a C++ desktop program developed by brothers Lars Rasmussen (software developer), Lars and Jens Eilstrup Rasmussen, Jens Rasmussen, Stephen Ma and Noel Gordon in Australia 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 and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ArcGIS
ArcGIS is a family of client, server and online geographic information system (GIS) software developed and maintained by Esri. ArcGIS was first released in 1982 as ARC/INFO, a command line-based GIS. ARC/INFO was later merged into ArcGIS Desktop, which was eventually superseded by ArcGIS Pro in 2015. Additionally, ArcGIS Server is a server-side GIS and geodata sharing software. Product history Prior to the ArcGIS suite, Esri had focused its software development on the command line Arc/INFO workstation program and several graphical user interface-based products such as the ArcView GIS 3.x desktop program. Other Esri products included MapObjects, a programming library for developers, and ArcSDE as a relational database management system. The various products had branched out into multiple source trees and did not integrate well with one another. In January 1997, Esri decided to revamp its GIS software platform, creating a single integrated software architecture. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GRASS GIS
''Geographic Resources Analysis Support System'' (commonly termed ''GRASS GIS'') is a geographic information system (GIS) software suite used for geospatial data management and analysis, image processing, producing graphics and maps, spatial and temporal modeling, and visualizing. It can handle raster, topological vector, image processing, and graphic data. GRASS contains over 350 modules to render maps and images on monitor and paper; manipulate raster and vector data including vector networks; process multispectral image data; and create, manage, and store spatial data. It is licensed and released as free and open-source software under the GNU General Public License (GPL). It runs on multiple operating systems, including , Windows and Linux. Users can interface with the software features through a graphical user interface (GUI) or by ''plugging into'' GRASS via other software such as QGIS. They can also interface with the modules directly through a bespoke shell that the appl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
