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Fractional Cascading
In computer science, fractional cascading is a technique to speed up a sequence of binary searches for the same value in a sequence of related data structures. The first binary search in the sequence takes a logarithmic amount of time, as is standard for binary searches, but successive searches in the sequence are faster. The original version of fractional cascading, introduced in two papers by Chazelle and Guibas in 1986 (; ), combined the idea of cascading, originating in range searching data structures of and , with the idea of fractional sampling, which originated in . Later authors introduced more complex forms of fractional cascading that allow the data structure to be maintained as the data changes by a sequence of discrete insertion and deletion events. Example As a simple example of fractional cascading, consider the following problem. We are given as input a collection of k ordered lists L_i of numbers, such that the total length \sum_i , L_i, of all lists is n, and mus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, applied disciplines (including the design and implementation of Computer architecture, hardware and Software engineering, software). Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and preventing security vulnerabilities. Computer graphics (computer science), 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 re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Range Reporting
In computational geometry and database theory, a range reporting query asks for a list of the points that match the query. The query is often specified by a geometric shape, containing all the points that should match, and is called a range. Range reporting is a special case of range searching, in which queries may return other kinds of aggregate information about points in a range. Range reporting queries are often handled by building a data structure from a collection of points that can answer queries efficiently. Because the worst case output size for a range reporting query, measured as a function of the data set size , can be itself, much of the research on range reporting data structures has investigated output-sensitive algorithms, where the query time is analyzed in terms of both and the number of reported points (often denoted ). For example, for one-dimensional (numeric) data with query ranges that are intervals, range reporting queries can be handled by storing the d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Data Structures
Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties * Graph (topology), a topological space resembling a graph in the sense of discrete mathematics *Graph of a function * Graph of a relation * Graph paper *Chart, a means of representing data (also called a graph) Computing *Graph (abstract data type), an abstract data type representing relations or connections * graph (Unix), Unix command-line utility * Conceptual graph, a model for knowledge representation and reasoning *Microsoft Graph, a Microsoft API developer platform that connects multiple services and devices Other uses * HMS ''Graph'', a submarine of the UK Royal Navy See also * Complex network *Graf *Graff (other) *Graph database *Grapheme, in linguistics *Graphemics *Graphic (other) *-graphy (suffix from the Greek for "describe," "write" or "draw") * List of information graphics software *S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sensor Network
Wireless sensor networks (WSNs) refer to networks of spatially dispersed and dedicated sensors that monitor and record the physical conditions of the environment and forward the collected data to a central location. WSNs can measure environmental conditions such as temperature, sound, pollution levels, humidity and wind. These are similar to wireless ad hoc network A wireless ad hoc network (WANET) or mobile ad hoc network (MANET) is a decentralized type of wireless network. The network is ad hoc because it does not rely on a pre-existing infrastructure, such as routers or wireless access points. Instead, ...s in the sense that they rely on wireless connectivity and spontaneous formation of networks so that sensor data can be transported wirelessly. WSNs monitor physical conditions, such as temperature, sound, and pressure. Modern networks are bi-directional, both collecting data and enabling control of sensor activity. The development of these networks was motivated by mil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internet Router
A router is a computer and networking device that forwards data packets between computer networks, including internetworks such as the global Internet. Routers perform the "traffic directing" functions on the Internet. A router is connected to two or more data lines from different IP networks. When a data packet comes in on a line, the router reads the network address information in the packet header to determine the ultimate destination. Then, using information in its routing table or routing policy, it directs the packet to the next network on its journey. Data packets are forwarded from one router to another through an internetwork until it reaches its destination node. The most familiar type of IP routers are home and small office routers that forward IP packets between the home computers and the Internet. More sophisticated routers, such as enterprise routers, connect large business or ISP networks to powerful core routers that forward data at high speed along the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Packet Filter
In computing, a firewall is a network security system that monitors and controls incoming and outgoing network traffic based on configurable security rules. A firewall typically establishes a barrier between a trusted network and an untrusted network, such as the Internet or between several VLANs. Firewalls can be categorized as network-based or host-based. History The term ''firewall'' originally referred to a wall to confine a fire within a line of adjacent buildings. Later uses refer to similar structures, such as the metal sheet separating the engine compartment of a vehicle or aircraft from the passenger compartment. The term was applied in the 1980s to network technology that emerged when the Internet was fairly new in terms of its global use and connectivity. The predecessors to firewalls for network security were routers used in the 1980s. Because they already segregated networks, routers could filter packets crossing them. Before it was used in real-life computing, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Point Location
The point location problem is a fundamental topic of computational geometry. It finds applications in areas that deal with processing geometrical data: computer graphics, geographic information systems (GIS), motion planning, and computer aided design (CAD). In its most general form, the problem is, given a partition of the space into disjoint regions, to determine the region where a query point lies. For example, the problem of determining which window of a graphical user interface contains a given mouse click can be formulated as an instance of point location, with a subdivision formed by the visible parts of each window, although specialized data structures may be more appropriate than general-purpose point location data structures in this application. Another special case is the point in polygon problem, in which one needs to determine whether a point is inside, outside, or on the boundary of a single polygon. In many applications, one needs to determine the location of sev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sequential Search
In computer science, linear search or sequential search is a method for finding an element within a list. It sequentially checks each element of the list until a match is found or the whole list has been searched. A linear search runs in linear time in the worst case, and makes at most comparisons, where is the length of the list. If each element is equally likely to be searched, then linear search has an average case of comparisons, but the average case can be affected if the search probabilities for each element vary. Linear search is rarely practical because other search algorithms and schemes, such as the binary search algorithm and hash tables, allow significantly faster searching for all but short lists. Algorithm A linear search sequentially checks each element of the list until it finds an element that matches the target value. If the algorithm reaches the end of the list, the search terminates unsuccessfully. Basic algorithm Given a list of elements with values o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Hull
In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space, or equivalently as the set of all convex combinations of points in the subset. For a Bounded set, bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around the subset. Convex hulls of open sets are open, and convex hulls of compact sets are compact. Every compact convex set is the convex hull of its extreme points. The convex hull operator is an example of a closure operator, and every antimatroid can be represented by applying this closure operator to finite sets of points. The algorithmic problems of finding the convex hull of a finite set of points in the plane or other low-dimensional Euclidean spaces, and its projective duality, dual problem of intersecting Half-space (geome ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Polygon
In geometry, a convex polygon is a polygon that is the boundary of a convex set. This means that the line segment between two points of the polygon is contained in the union of the interior and the boundary of the polygon. In particular, it is a simple polygon (not self-intersecting). Equivalently, a polygon is convex if every line that does not contain any edge intersects the polygon in at most two points. Strictly convex polygon A convex polygon is ''strictly'' convex if no line contains more than two vertices of the polygon. In a convex polygon, all interior angles are less than ''or equal'' to 180 degrees, while in a strictly convex polygon all interior angles are strictly less than 180 degrees. Properties The following properties of a simple polygon are all equivalent to convexity: *Every internal angle is less than or equal to 180 degrees. *Every point on every line segment between two points inside or on the boundary of the polygon remains inside or on the bou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Layers
In computational geometry, the convex layers of a set of points in the Euclidean plane are a sequence of nested convex polygons having the points as their vertices. The outermost one is the convex hull of the points and the rest are formed in the same way recursively. The innermost layer may be degenerate, consisting only of one or two points. The problem of constructing convex layers has also been called onion peeling or onion decomposition. Although constructing the convex layers by repeatedly finding convex hulls would be slower, it is possible to partition any set of n points into its convex layers in time O(n\log n). An early application of the convex layers was in robust statistics, as a way of identifying outliers and measuring the central tendency of a set of sample points. In this context, the number of convex layers surrounding a given point is called its convex hull peeling depth, and the convex layers themselves are the depth contours for this notion of data depth. C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Half-plane
In mathematics, the upper half-plane, is the set of points in the Cartesian plane with The lower half-plane is the set of points with instead. Arbitrary oriented half-planes can be obtained via a planar rotation. Half-planes are an example of two-dimensional half-space. A half-plane can be split in two quadrants. Affine geometry The affine transformations of the upper half-plane include # shifts (x,y)\mapsto (x+c,y), c\in\mathbb, and # dilations (x,y)\mapsto (\lambda x,\lambda y), \lambda > 0. Proposition: Let and be semicircles in the upper half-plane with centers on the boundary. Then there is an affine mapping that takes A to B. :Proof: First shift the center of to Then take \lambda=(\text\ B)/(\text\ A) and dilate. Then shift to the center of Inversive geometry Definition: \mathcal := \left\ . can be recognized as the circle of radius centered at and as the polar plot of \rho(\theta) = \cos \theta. Proposition: in and are collinear points. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
