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Traveling Salesman Problem
The travelling salesman problem (also called the travelling salesperson problem or 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 and the vehicle routing problem are both generalizations of TSP. In the theory of computational complexity, the decision version of the TSP (where given a length ''L'', the task is to decide whether the graph has a tour of 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 p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GLPK Solution Of A Travelling Salesman Problem
The GNU Linear Programming Kit (GLPK) is a software package intended for solving large-scale linear programming (LP), mixed integer programming (MIP), and other related problems. It is a set of routines written in ANSI C and organized in the form of a callable library. The package is part of the GNU Project and is released under the GNU General Public License. Problems can be modeled in the language GNU MathProg (previously known as GMPL) which shares many parts of the syntax with AMPL and solved with standalone solver GLPSOL. GLPK can also be used as a C library. GLPK uses the revised simplex method and the primal-dual interior point method for non-integer problems and the branch-and-bound algorithm together with Gomory's mixed integer cuts for (mixed) integer problems. GLPK is supported in the free edition of the OptimJ modeling system An independent project provides a Java-based interface to GLPK (via JNI). This allows Java applications to call out to GLPK in a relativel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integrated Circuit
An integrated circuit or monolithic integrated circuit (also referred to as an IC, a chip, or a microchip) is a set of electronic circuits on one small flat piece (or "chip") of semiconductor material, usually silicon. Large numbers of tiny MOSFETs (metal–oxide–semiconductor field-effect transistors) integrate into a small chip. This results in circuits that are orders of magnitude smaller, faster, and less expensive than those constructed of discrete electronic components. The IC's mass production capability, reliability, and building-block approach to integrated circuit design has ensured the rapid adoption of standardized ICs in place of designs using discrete transistors. ICs are now used in virtually all electronic equipment and have revolutionized the world of electronics. Computers, mobile phones and other home appliances are now inextricable parts of the structure of modern societies, made possible by the small size and low cost of ICs such as modern computer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Merrill M
Merrill may refer to: Places in the United States *Merrill Field, Anchorage, Alaska *Merrill, Iowa * Merrill, Maine *Merrill, Michigan * Merrill, Mississippi, an unincorporated community near Lucedale in George County *Merrill, Oregon *Merrill, Wisconsin * Merrill (town), Wisconsin *Merrill Township, Michigan * Merrill Township, North Dakota *Merrill College at the University of California, Santa Cruz People * Merrill Moses (born 1977), Olympic water polo player *Merrill (surname) *Merrill Cook, Utah politician *Merrill Garbus, musician behind the experimental indie project Tune-yards *Merrill Ashley (born 1950), American ballet dancer and ''répétiteur'' Other uses *Merrill (company), a division of Bank of America *Skidmore, Owings and Merrill, architectural firm * USS ''Merrill'' (DD-976) *Nine men's morris, a strategy board game also called ''Merrills'' * Merrill (crater) Merrill is a lunar impact crater. It is located in the high northern latitudes, on the far side. Less th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karl Menger
Karl Menger (January 13, 1902 – October 5, 1985) was an Austrian-American mathematician, the son of the economist Carl Menger. In mathematics, Menger studied the theory of algebras and the dimension theory of low- regularity ("rough") curves and regions; in graph theory, he is credited with Menger's theorem. Outside of mathematics, Menger has substantial contributions to game theory and social sciences. Biography Karl Menger was a student of Hans Hahn and received his PhD from the University of Vienna in 1924. L. E. J. Brouwer invited Menger in 1925 to teach at the University of Amsterdam. In 1927, he returned to Vienna to accept a professorship there. In 1930 and 1931 he was visiting lecturer at Harvard University and the Rice Institute. From 1937 to 1946 he was a professor at the University of Notre Dame. From 1946 to 1971, he was a professor at Illinois Institute of Technology (IIT) in Chicago. In 1983, IIT awarded Menger a Doctor of Humane Letters and Sciences degree. C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Theory, 1736–1936
''Graph Theory, 1736–1936'' is a book in the history of mathematics on graph theory. It focuses on the foundational documents of the field, beginning with the 1736 paper of Leonhard Euler on the Seven Bridges of Königsberg and ending with the first textbook on the subject, published in 1936 by Dénes Kőnig. ''Graph Theory, 1736–1936'' was edited by Norman L. Biggs, E. Keith Lloyd, and Robin J. Wilson, and published in 1976 by the Clarendon Press. The Oxford University Press published a paperback second edition in 1986, with a corrected reprint in 1998. Topics ''Graph Theory, 1736–1936'' contains copies, extracts, and translations of 37 original sources in graph theory, grouped into ten chapters and punctuated by commentary on their meaning and context. It begins with Euler's 1736 paper "Solutio problematis ad geometriam situs pertinentis" on the seven bridges of Königsberg (both in the original Latin and in English translation) and ending with Dénes Kőnig's book ''Theo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamiltonian Path
In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a cycle that visits each vertex exactly once. A Hamiltonian path that starts and ends at adjacent vertices can be completed by adding one more edge to form a Hamiltonian cycle, and removing any edge from a Hamiltonian cycle produces a Hamiltonian path. Determining whether such paths and cycles exist in graphs (the Hamiltonian path problem and Hamiltonian cycle problem) are NP-complete. Hamiltonian paths and cycles are named after William Rowan Hamilton who invented the icosian game, now also known as ''Hamilton's puzzle'', which involves finding a Hamiltonian cycle in the edge graph of the dodecahedron. Hamilton solved this problem using the icosian calculus, an algebraic structure based on roots of unity with many similarities to the quaternions (also invented by Hami ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Icosian Game
The icosian game is a mathematical game invented in 1857 by William Rowan Hamilton. The game's object is finding a Hamiltonian cycle along the edges of a dodecahedron such that every vertex is visited a single time, and the ending point is the same as the starting point. The puzzle was distributed commercially as a pegboard with holes at the nodes of the dodecahedral graph and was subsequently marketed in Europe in many forms. The motivation for Hamilton was the problem of symmetries of an icosahedron, for which he invented icosian calculus—an algebraic tool to compute the symmetries. The solution of the puzzle is a cycle containing twenty (in ancient Greek ''icosa'') edges (i.e. a Hamiltonian circuit on the dodecahedron). See also * Hunt the Wumpus * Dual polyhedron * Seven Bridges of Königsberg The Seven Bridges of Königsberg is a historically notable problem in mathematics. Its negative resolution by Leonhard Euler in 1736 laid the foundations of graph theory and pre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomas Kirkman
Thomas Penyngton Kirkman FRS (31 March 1806 – 3 February 1895) was a British mathematician and ordained minister of the Church of England. Despite being primarily a churchman, he maintained an active interest in research-level mathematics, and was listed by Alexander Macfarlane as one of ten leading 19th-century British mathematicians... In the 1840s, he obtained an existence theorem for Steiner triple systems that founded the field of combinatorial design theory, while the related Kirkman's schoolgirl problem is named after him. Early life and education Kirkman was born 31 March 1806 in Bolton, in the north west of England, the son of a local cotton dealer. In his schooling at the Bolton Grammar School, he studied classics, but no mathematics was taught in the school. He was recognised as the best scholar at the school, and the local vicar guaranteed him a scholarship at Cambridge, but his father would not allow him to go. Instead, he left school at age 14 to work in his fat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Rowan Hamilton
Sir William Rowan Hamilton Doctor of Law, LL.D, Doctor of Civil Law, DCL, Royal Irish Academy, MRIA, Royal Astronomical Society#Fellow, FRAS (3/4 August 1805 – 2 September 1865) was an Irish mathematician, astronomer, and physicist. He was the Andrews Professor of Astronomy at Trinity College Dublin, and Royal Astronomer of Ireland, living at Dunsink Observatory. Hamilton's scientific career included the study of geometrical optics, ideas from Fourier analysis, and his work on quaternions which made him one of the founders of modern linear algebra. He made major contributions in optics, classical mechanics and abstract algebra. His work was fundamental to modern theoretical physics, particularly his reformulation of Newtonian mechanics, now called Hamiltonian mechanics. It is now central both to electromagnetism and to quantum mechanics. Early life Hamilton was the fourth of nine children born to Sarah Hutton (1780–1817) and Archibald Hamilton (1778–1819),Bruno (2003) who ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Rowan Hamilton Painting
William is a male given name of Germanic origin.Hanks, Hardcastle and Hodges, ''Oxford Dictionary of First Names'', Oxford University Press, 2nd edition, , p. 276. It became very popular in the English language after the Norman conquest of England in 1066,All Things William"Meaning & Origin of the Name"/ref> and remained so throughout the Middle Ages and into the modern era. It is sometimes abbreviated "Wm." Shortened familiar versions in English include Will, Wills, Willy, Willie, Bill, and Billy. A common Irish form is Liam. Scottish diminutives include Wull, Willie or Wullie (as in Oor Wullie or the play ''Douglas''). Female forms are Willa, Willemina, Wilma and Wilhelmina. Etymology William is related to the given name ''Wilhelm'' (cf. Proto-Germanic ᚹᛁᛚᛃᚨᚺᛖᛚᛗᚨᛉ, ''*Wiljahelmaz'' > German ''Wilhelm'' and Old Norse ᚢᛁᛚᛋᛅᚼᛅᛚᛘᛅᛋ, ''Vilhjálmr''). By regular sound changes, the native, inherited English form of the name should b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Switzerland
). Swiss law does not designate a ''capital'' as such, but the federal parliament and government are installed in Bern, while other federal institutions, such as the federal courts, are in other cities (Bellinzona, Lausanne, Luzern, Neuchâtel, St. Gallen a.o.). , coordinates = , largest_city = Zürich , official_languages = , englishmotto = "One for all, all for one" , religion_year = 2020 , religion_ref = , religion = , demonym = , german: Schweizer/Schweizerin, french: Suisse/Suissesse, it, svizzero/svizzera or , rm, Svizzer/Svizra , government_type = Federalism, Federal assembly-independent Directorial system, directorial republic with elements of a direct democracy , leader_title1 = Federal Council (Switzerland), Federal Council , leader_name1 = , leader_title2 = , leader_name2 = Walter Thurnherr , legislature = Fe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Germany
Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated between the Baltic and North seas to the north, and the Alps to the south; it covers an area of , with a population of almost 84 million within its 16 constituent states. Germany borders Denmark to the north, Poland and the Czech Republic to the east, Austria and Switzerland to the south, and France, Luxembourg, Belgium, and the Netherlands to the west. The nation's capital and most populous city is Berlin and its financial centre is Frankfurt; the largest urban area is the Ruhr. Various Germanic tribes have inhabited the northern parts of modern Germany since classical antiquity. A region named Germania was documented before AD 100. In 962, the Kingdom of Germany formed the bulk of the Holy Roman Empire. During the 16th ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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