|
Arc Diagram
An arc diagram is a style of graph drawing, in which the vertices of a graph are placed along a line in the Euclidean plane and edges are drawn using semicircles or other convex curves above or below the line. These drawings are also called linear embeddings or circuit diagrams. Applications of arc diagrams include information visualization, the Farey diagram of number-theoretic connections between rational numbers, and diagrams representing RNA secondary structure in which the crossings of the diagram represent pseudoknots in the structure. Description In an arc diagram, the vertices of a graph are arranged along a line in the Euclidean plane. The edges are drawn as semicircles in one or both of the two halfplanes bounded by the line, or as smooth curves formed by sequences of semicircles. In some cases, line segments of the line itself are also allowed as edges, as long as they connect only vertices that are consecutive along the line. Variations of this drawing style in whic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Goldner–Harary Graph
In the mathematics, mathematical field of graph theory, the Goldner–Harary graph is a simple undirected graph with 11 vertices and 27 edges. It is named after Anita M. Goldner and Frank Harary, who proved in 1975 that it was the smallest Hamiltonian graph, non-Hamiltonian maximal planar graph. The same graph had already been given as an example of a non-Hamiltonian simplicial polyhedron by Branko Grünbaum in 1967. Properties The Goldner–Harary graph is a planar graph: it can be drawn in the plane with none of its edges crossing. When drawn on a plane, all its faces are triangular, making it a maximal planar graph. As with every maximal planar graph, it is also vertex connectivity, 3-vertex-connected: the removal of any two of its vertices leaves a connected Glossary of graph theory#Subgraphs, subgraph. The Goldner–Harary graph is also hamiltonian graph, non-Hamiltonian. The smallest possible number of vertices for a non-Hamiltonian polyhedral graph, polyhedral graph is 11. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Farey Diagram Horizontal Arc 9
Farey is the surname of: * Cyril Farey (1888–1954), British architect and architectural illustrator * John Farey Sr. (1766–1826), English geologist * John Farey Jr. (1791–1851), English mechanical engineer, son of John Farey Sr. * Joseph Farey (1796–1829), English mechanical engineer and draughtsman, son of John Farey Sr. * Lizzie Farey (born 1962), Scottish artist See also *Farey sequence, a mathematical construct named after John Farey Sr. {{Surname, Farey ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Football
American football, referred to simply as football in the United States and Canada and also known as gridiron football, is a team sport played by two teams of eleven players on a rectangular American football field, field with goalposts at each end. The offense (sports), offense, the team with possession of the oval-shaped Ball (gridiron football), football, attempts to advance down the field by Rush (gridiron football), running with the ball or Forward pass#Gridiron football, throwing it, while the Defense (sports), defense, the team without possession of the ball, aims to stop the offense's advance and to take control of the ball for themselves. The offense must advance the ball at least ten yard, yards in four Down (gridiron football), downs or plays; if they fail, they turnover on downs, turn over the football to the defense, but if they succeed, they are given a new set of four downs to continue the Glossary of American football#drive, drive. Points are scored primarily b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bluetooth
Bluetooth is a short-range wireless technology standard that is used for exchanging data between fixed and mobile devices over short distances and building personal area networks (PANs). In the most widely used mode, transmission power is limited to 2.5 milliwatts, giving it a very short range of up to . It employs Ultra high frequency, UHF radio waves in the ISM bands, from 2.402GHz to 2.48GHz. It is mainly used as an alternative to wired connections to exchange files between nearby portable devices and connect cell phones and music players with wireless headphones, wireless speakers, HIFI systems, car audio and wireless transmission between TVs and soundbars. Bluetooth is managed by the Bluetooth Special Interest Group (SIG), which has more than 35,000 member companies in the areas of telecommunication, computing, networking, and consumer electronics. The Institute of Electrical and Electronics Engineers, IEEE standardized Bluetooth as IEEE 802.15.1 but no longer maintains ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cutwidth
In graph theory, the cutwidth of an undirected graph is the smallest integer k with the following property: there is an ordering of the vertices of the graph, such that every cut obtained by partitioning the vertices into earlier and later subsets of the ordering is crossed by at most k edges. That is, if the vertices are numbered v_1,v_2,\dots v_n, then for every \ell=1,2,\dots n-1, the number of edges v_iv_j with i\le\ell and j>\ell is at most k. The cutwidth of a graph has also been called its folding number. Both the vertex ordering that produces the cutwidth, and the problem of computing this ordering and the cutwidth, have been called minimum cut linear arrangement. Relation to other parameters Cutwidth is related to several other width parameters of graphs. In particular, it is always at least as large as the treewidth or pathwidth of the same graph. However, it is at most the pathwidth multiplied by O(\Delta), or the treewidth multiplied by O(\Delta\log n) where \Delta i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shift Register
A shift register is a type of digital circuit using a cascade of flip-flop (electronics), flip-flops where the output of one flip-flop is connected to the input of the next. They share a single clock signal, which causes the data stored in the system to shift from one location to the next. By connecting the last flip-flop back to the first, the data can cycle within the shifters for extended periods, and in this configuration they were used as computer memory, displacing delay-line memory systems in the late 1960s and early 1970s. In most cases, several parallel shift registers would be used to build a larger memory pool known as a "bit array". Data was stored into the array and read back out in parallel, often as a computer word, while each bit was stored serially in the shift registers. There is an inherent trade-off in the design of bit arrays; putting more flip-flops in a row allows a single shifter to store more bits, but requires more clock cycles to push the data through all ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
State Diagram
A state diagram is used in computer science and related fields to describe the behavior of systems. State diagrams require that the system is composed of a finite number of states. Sometimes, this is indeed the case, while at other times this is a reasonable abstraction. Many forms of state diagrams exist, which differ slightly and have different semantics. Overview State diagrams provide an abstract description of a system's behavior. This behavior is analyzed and represented by a series of events that can occur in one or more possible states. Hereby "each diagram usually represents objects of a single class and track the different states of its objects through the system". State diagrams can be used to graphically represent finite-state machines (also called finite automata). This was introduced by Claude Shannon and Warren Weaver in their 1949 book ''The Mathematical Theory of Communication''. Another source is Taylor Booth in his 1967 book ''Sequential Machines and Aut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Cut
In a graph, a maximum cut is a cut whose size is at least the size of any other cut. That is, it is a partition of the graph's vertices into two complementary sets and , such that the number of edges between and is as large as possible. Finding such a cut is known as the max-cut problem. The problem can be stated simply as follows. One wants a subset of the vertex set such that the number of edges between and the complementary subset is as large as possible. Equivalently, one wants a bipartite subgraph of the graph with as many edges as possible. There is a more general version of the problem called weighted max-cut, where each edge is associated with a real number, its weight, and the objective is to maximize the total weight of the edges between and its complement rather than the number of the edges. The weighted max-cut problem allowing both positive and negative weights can be trivially transformed into a weighted minimum cut problem by flipping the sign in all ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Approximation Algorithm
In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to optimization problems (in particular NP-hard problems) with provable guarantees on the distance of the returned solution to the optimal one. Approximation algorithms naturally arise in the field of theoretical computer science as a consequence of the widely believed P ≠ NP conjecture. Under this conjecture, a wide class of optimization problems cannot be solved exactly in polynomial time. The field of approximation algorithms, therefore, tries to understand how closely it is possible to approximate optimal solutions to such problems in polynomial time. In an overwhelming majority of the cases, the guarantee of such algorithms is a multiplicative one expressed as an approximation ratio or approximation factor i.e., the optimal solution is always guaranteed to be within a (predetermined) multiplicative factor of the returned solution. However, there a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2-satisfiability
In computer science, 2-satisfiability, 2-SAT or just 2SAT is a computational problem of assigning values to variables, each of which has two possible values, in order to satisfy a system of constraints on pairs of variables. It is a special case of the general Boolean satisfiability problem, which can involve constraints on more than two variables, and of constraint satisfaction problems, which can allow more than two choices for the value of each variable. But in contrast to those more general problems, which are NP-complete, 2-satisfiability can be solved in polynomial time. Instances of the 2-satisfiability problem are typically expressed as Boolean formulas of a special type, called conjunctive normal form (2-CNF) or Krom formulas. Alternatively, they may be expressed as a special type of directed graph, the implication graph, which expresses the variables of an instance and their negations as vertices in a graph, and constraints on pairs of variables as directed edges. Both ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NP-hard
In computational complexity theory, a computational problem ''H'' is called NP-hard if, for every problem ''L'' which can be solved in non-deterministic polynomial-time, there is a polynomial-time reduction from ''L'' to ''H''. That is, assuming a solution for ''H'' takes 1 unit time, ''H''s solution can be used to solve ''L'' in polynomial time. As a consequence, finding a polynomial time algorithm to solve a single NP-hard problem would give polynomial time algorithms for all the problems in the complexity class NP. As it is suspected, but unproven, that P≠NP, it is unlikely that any polynomial-time algorithms for NP-hard problems exist. A simple example of an NP-hard problem is the subset sum problem. Informally, if ''H'' is NP-hard, then it is at least as difficult to solve as the problems in NP. However, the opposite direction is not true: some problems are undecidable, and therefore even more difficult to solve than all problems in NP, but they are probably not NP- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
