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Bellman–Ford Algorithm
The Bellman–Ford algorithm is an algorithm that computes shortest paths from a single source vertex (graph theory), vertex to all of the other vertices in a weighted digraph. It is slower than Dijkstra's algorithm for the same problem, but more versatile, as it is capable of handling graphs in which some of the edge weights are negative numbers.Lecture 14 stanford.edu The algorithm was first proposed by , but is instead named after Richard Bellman and L. R. Ford Jr., Lester Ford Jr., who published it in #, 1958 and #, 1956, respectively. Edward F. Moore also published a variation of the algorithm in #, 1959, and for this reason it is also sometimes called the Bellman–Ford–Moore algorithm. Negative edge weights are found in various applications of graph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cycle Detection
In computer science, cycle detection or cycle finding is the algorithmic problem of finding a cycle in a sequence of iterated function values. For any function that maps a finite set to itself, and any initial value in , the sequence of iterated function values : x_0,\ x_1=f(x_0),\ x_2=f(x_1),\ \dots,\ x_i=f(x_),\ \dots must eventually use the same value twice: there must be some pair of distinct indices and such that . Once this happens, the sequence must continue periodically, by repeating the same sequence of values from to . Cycle detection is the problem of finding and , given and . Several algorithms are known for finding cycles quickly and with little memory. Robert W. Floyd's tortoise and hare algorithm moves two pointers at different speeds through the sequence of values until they both point to equal values. Alternatively, Brent's algorithm is based on the idea of exponential search. Both Floyd's and Brent's algorithms use only a constant number of memor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Complexity
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 gene ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Georgetown University
Georgetown University is a private university, private Jesuit research university in Washington, D.C., United States. Founded by Bishop John Carroll (archbishop of Baltimore), John Carroll in 1789, it is the oldest Catholic higher education, Catholic institution of higher education in the United States, the oldest university in Washington, D.C., and the nation's first University charter#Federal, federally chartered university. The university has eleven Undergraduate education, undergraduate and Postgraduate education, graduate schools. Its main campus, located in the Georgetown (Washington, D.C.), Georgetown historic neighborhood, is on a hill above the Potomac River and identifiable by Healy Hall, a National Historic Landmark. It is Carnegie Classification of Institutions of Higher Education, classified among List_of_research_universities_in_the_United_States#Universities_classified_as_"R1:_Doctoral_Universities_–_Very_high_research_activity", "R1: Doctoral Universities – V ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expected Value
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first Moment (mathematics), moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean, mean of the possible values a random variable can take, weighted by the probability of those outcomes. Since it is obtained through arithmetic, the expected value sometimes may not even be included in the sample data set; it is not the value you would expect to get in reality. The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by Integral, integration. In the axiomatic foundation for probability provided by measure theory, the expectation is given by Lebesgue integration. The expected value of a random variable is often denoted by , , or , with a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Permutation
A random permutation is a sequence where any order of its items is equally likely at random, that is, it is a permutation-valued random variable of a set of objects. The use of random permutations is common in games of chance and in randomized algorithms in coding theory, cryptography, and simulation. A good example of a random permutation is the fair shuffling of a standard deck of cards: this is ideally a random permutation of the 52 cards. Computation of random permutations Entry-by-entry methods One algorithm for generating a random permutation of a set of size ''n'' uniformly at random, i.e., such that each of the ''n''! permutations is equally likely to appear, is to generate a sequence by uniformly randomly selecting an integer between 1 and ''n'' (inclusive), sequentially and without replacement ''n'' times, and then to interpret this sequence (''x''1, ..., ''x''''n'') as the permutation : \begin 1 & 2 & 3 & \cdots & n \\ x_1 & x_2 & x_3 & \cdots & x_n \\ \end, shown h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dense Graph
In mathematics, a dense graph is a graph in which the number of edges is close to the maximal number of edges (where every pair of vertices is connected by one edge). The opposite, a graph with only a few edges, is a sparse graph. The distinction of what constitutes a dense or sparse graph is ill-defined, and is often represented by 'roughly equal to' statements. Due to this, the way that density is defined often depends on the context of the problem. The graph density of simple graphs is defined to be the ratio of the number of edges with respect to the maximum possible edges. For undirected simple graphs, the graph density is: :D = \frac = \frac For directed, simple graphs, the maximum possible edges is twice that of undirected graphs (as there are two directions to an edge) so the density is: :D = \frac = \frac where is the number of edges and is the number of vertices in the graph. The maximum number of edges for an undirected graph is = \frac2, so the maximal density is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distance-vector Routing Protocol
A distance-vector routing protocol in data networks determines the best route for data packets based on distance. Distance-vector routing protocols measure the distance by the number of routers a packet has to pass; one router counts as one hop. Some distance-vector protocols also take into account network latency and other factors that influence traffic on a given route. To determine the best route across a network, routers using a distance-vector protocol exchange information with one another, usually routing tables plus hop counts for destination networks and possibly other traffic information. Distance-vector routing protocols also require that a router inform its neighbours of network topology changes periodically. Distance-vector routing protocols use the Bellman–Ford algorithm to calculate the best route. Another way of calculating the best route across a network is based on link cost, and is implemented through link-state routing protocols. The term ''distance vec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Network Topology
Network topology is the arrangement of the elements (Data link, links, Node (networking), nodes, etc.) of a communication network. Network topology can be used to define or describe the arrangement of various types of telecommunication networks, including command and control radio networks, industrial Fieldbus, fieldbusses and computer networks. Network topology is the topological structure of a network and may be depicted physically or logically. It is an application of graph theory wherein communicating devices are modeled as nodes and the connections between the devices are modeled as links or lines between the nodes. Physical topology is the placement of the various components of a network (e.g., device location and cable installation), while logical topology illustrates how data flows within a network. Distances between nodes, physical interconnections, transmission rates, or signal types may differ between two different networks, yet their logical topologies may be identica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Autonomous System (Internet)
An autonomous system (AS) is a collection of connected Internet protocol address, Internet Protocol (IP) routing prefixes under the control of one or more network operators on behalf of a single administrative entity or domain, that presents a common and clearly defined routing policy to the Internet. Each AS is assigned an autonomous system number (ASN), for use in Border Gateway Protocol (BGP) routing. Autonomous System Numbers are assigned to Regional_Internet_registry#Local_Internet_registry, local Internet registries (LIRs) and end-user organizations by their respective Regional Internet registry, regional Internet registries (RIRs), which in turn receive blocks of ASNs for reassignment from the Internet Assigned Numbers Authority (IANA). The IANA also maintains a registry of ASNs which are reserved for private use (and should therefore not be announced to the global Internet). Originally, the definition required control by a single entity, typically an Internet service provid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Routing Information Protocol
The Routing Information Protocol (RIP) is one of the oldest distance-vector routing protocols which employs the hop count as a routing metric. RIP prevents routing loops by implementing a limit on the number of hops allowed in a path from source to destination. The largest number of hops allowed for RIP is 15, which limits the size of networks that RIP can support. RIP implements the split horizon, route poisoning, and holddown mechanisms to prevent incorrect routing information from being propagated. In RIPv1 routers broadcast updates with their routing table every 30 seconds. In the early deployments, routing tables were small enough that the traffic was not significant. As networks grew in size, however, it became evident there could be a massive traffic burst every 30 seconds, even if the routers had been initialized at random times. In most networking environments, RIP is not the preferred choice of routing protocol, as its time to converge and scalability are poo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distance-vector Routing Protocol
A distance-vector routing protocol in data networks determines the best route for data packets based on distance. Distance-vector routing protocols measure the distance by the number of routers a packet has to pass; one router counts as one hop. Some distance-vector protocols also take into account network latency and other factors that influence traffic on a given route. To determine the best route across a network, routers using a distance-vector protocol exchange information with one another, usually routing tables plus hop counts for destination networks and possibly other traffic information. Distance-vector routing protocols also require that a router inform its neighbours of network topology changes periodically. Distance-vector routing protocols use the Bellman–Ford algorithm to calculate the best route. Another way of calculating the best route across a network is based on link cost, and is implemented through link-state routing protocols. The term ''distance vec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
