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Jenő Egerváry
Jenő Elek Egerváry (April 16, 1891 – November 30, 1958) was a Hungarian mathematician. Biography Egerváry was born in Debrecen in 1891. In 1914, he received his doctorate at the Pázmány Péter University in Budapest, where he studied under the supervision of Lipót Fejér. He then worked as an assistant at the Seismological Observatory in Budapest, and since 1918 as a professor at the Superior Industrial School in Budapest. In 1938 he was appointed Privatdozent at the Pázmány Péter University in Budapest. In 1941 he became full professor at the Technical University of Budapest, and in 1950 he was appointed Chairman of the Scientific Council of the Research Institute for Applied Mathematics of the Hungarian Academy of Sciences. Egerváry received the Gyula Kőnig Prize in 1932 and the Kossuth Prize in 1949 and 1953. He committed suicide in 1958 because of the troubles caused to him by the communist bureaucracy. Works Egerváry's interests spanned the theory of alg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Debrecen
Debrecen ( , is Hungary's second-largest city, after Budapest, the regional centre of the Northern Great Plain region and the seat of Hajdú-Bihar County. A city with county rights, it was the largest Hungarian city in the 18th century and it is one of the Hungarian people's most important cultural centres.Antal Papp: Magyarország (Hungary), Panoráma, Budapest, 1982, , p. 860, pp. 463-477 Debrecen was also the capital city of Hungary during the revolution in 1848–1849. During the revolution, the dethronement of the Habsburg dynasty was declared in the Reformed Great Church. The city also served as the capital of Hungary by the end of World War II in 1944–1945. It is home of the University of Debrecen. Etymology The city is first documented in 1235, as ''Debrezun''. The name derives from the Turkic word , which means 'live' or 'move' and is also a male given name. Another theory says the name is of Slavic origin and means 'well-esteemed', from Slavic Dьbricinъ or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theory Of Equations
In algebra, the theory of equations is the study of algebraic equations (also called "polynomial equations"), which are equations defined by a polynomial. The main problem of the theory of equations was to know when an algebraic equation has an algebraic solution. This problem was completely solved in 1830 by Évariste Galois, by introducing what is now called Galois theory. Before Galois, there was no clear distinction between the "theory of equations" and "algebra". Since then algebra has been dramatically enlarged to include many new subareas, and the theory of algebraic equations receives much less attention. Thus, the term "theory of equations" is mainly used in the context of the history of mathematics, to avoid confusion between old and new meanings of "algebra". History Until the end of the 19th century, "theory of equations" was almost synonymous with "algebra". For a long time, the main problem was to find the solutions of a single non-linear polynomial equation in a s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1891 Births
Events January–March * January 1 ** Paying of old age pensions begins in Germany. ** A strike of 500 Hungarian steel workers occurs; 3,000 men are out of work as a consequence. **Germany takes formal possession of its new African territories. * January 2 – A. L. Drummond of New York is appointed Chief of the Treasury Secret Service. * January 4 – The Earl of Zetland issues a declaration regarding the famine in the western counties of Ireland. * January 5 **The Australian shearers' strike, that leads indirectly to the foundation of the Australian Labor Party, begins. **A fight between the United States and Indians breaks out near Pine Ridge agency. ** Henry B. Brown, of Michigan, is sworn in as an Associate Justice of the Supreme Court. **A fight between railway strikers and police breaks out at Motherwell, Scotland. * January 6 – Encounters continue, between strikers and the authorities at Glasgow. * January 7 ** General Miles' force ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph
*Graf
*Graff (other)
*Graph database
*Grapheme, in ...
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 Other uses * HMS ''Graph'', a submarine of the UK Royal Navy See also *Complex network In the context of network theory, a complex network is a graph (network) with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in networks representing real s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hungarian Method
The Hungarian method is a combinatorial optimization algorithm that solves the assignment problem in polynomial time and which anticipated later primal–dual methods. It was developed and published in 1955 by Harold Kuhn, who gave the name "Hungarian method" because the algorithm was largely based on the earlier works of two Hungarian mathematicians: Dénes Kőnig and Jenő Egerváry.Harold W. Kuhn, "The Hungarian Method for the assignment problem", ''Naval Research Logistics Quarterly'', 2: 83–97, 1955. Kuhn's original publication.Harold W. Kuhn, "Variants of the Hungarian method for assignment problems", ''Naval Research Logistics Quarterly'', 3: 253–258, 1956. James Munkres reviewed the algorithm in 1957 and observed that it is (strongly) polynomial.J. Munkres, "Algorithms for the Assignment and Transportation Problems", ''Journal of the Society for Industrial and Applied Mathematics'', 5(1):32–38, 1957 March. Since then the algorithm has been known also as the Kuhn†... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Assignment Problem
The assignment problem is a fundamental combinatorial optimization problem. In its most general form, the problem is as follows: :The problem instance has a number of ''agents'' and a number of ''tasks''. Any agent can be assigned to perform any task, incurring some ''cost'' that may vary depending on the agent-task assignment. It is required to perform as many tasks as possible by assigning at most one agent to each task and at most one task to each agent, in such a way that the ''total cost'' of the assignment is minimized. Alternatively, describing the problem using graph theory: :The assignment problem consists of finding, in a weighted bipartite graph, a matching of a given size, in which the sum of weights of the edges is minimum. If the numbers of agents and tasks are equal, then the problem is called ''balanced assignment''. Otherwise, it is called ''unbalanced assignment''. If the total cost of the assignment for all tasks is equal to the sum of the costs for each agent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dénes Kőnig
Dénes Kőnig (September 21, 1884 – October 19, 1944) was a Hungarian mathematician of Jewish heritage who worked in and wrote the first textbook on the field of graph theory. Biography Kőnig was born in Budapest, the son of mathematician Gyula Kőnig. In 1907, he received his doctorate Translated by Richard McCoart; with commentary by W.T. Tutte. at, and joined the faculty of the Royal Joseph University in Budapest (today Budapest University of Technology and Economics). His classes were visited by Paul Erdős, who, as a first year student, solved one of his problems. Kőnig became a full professor there in 1935. To honor his fathers' death in 1913, Kőnig and his brother György created the Gyula Kőnig prize in 1918. This prize was meant to be an endowment for young mathematicians, however was later devaluated. But the prize remained as a medal of high scientific recognition. In 1899, he published his first work while still attending High School in a journal ''Matematikai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harold W
Harold may refer to: People * Harold (given name), including a list of persons and fictional characters with the name * Harold (surname), surname in the English language * András Arató, known in meme culture as "Hide the Pain Harold" Arts and entertainment * ''Harold'' (film), a 2008 comedy film * ''Harold'', an 1876 poem by Alfred, Lord Tennyson * ''Harold, the Last of the Saxons'', an 1848 book by Edward Bulwer-Lytton, 1st Baron Lytton * ''Harold or the Norman Conquest'', an opera by Frederic Cowen * ''Harold'', an 1885 opera by Eduard NápravnÃk * Harold, a character from the cartoon ''The Grim Adventures of Billy & Mandy'' *Harold & Kumar, a US movie; Harold/Harry is the main actor in the show. Places ;In the United States * Alpine, Los Angeles County, California, an erstwhile settlement that was also known as Harold * Harold, Florida, an unincorporated community * Harold, Kentucky, an unincorporated community * Harold, Missouri, an unincorporated community ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph (discrete Mathematics)
In discrete mathematics, and more specifically in graph theory, a graph is a structure amounting to a Set (mathematics), set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called ''Vertex (graph theory), vertices'' (also called ''nodes'' or ''points'') and each of the related pairs of vertices is called an ''edge'' (also called ''link'' or ''line''). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics. The edges may be directed or undirected. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person ''A'' can shake hands with a person ''B'' only if ''B'' also shakes hands with ''A''. In contrast, if an edge from a person ''A'' to a person ''B'' m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
KÅ‘nig's Theorem (graph Theory)
In the mathematical area of graph theory, Kőnig's theorem, proved by , describes an equivalence between the maximum matching problem and the minimum vertex cover problem in bipartite graphs. It was discovered independently, also in 1931, by Jenő Egerváry in the more general case of weighted graphs. Setting A vertex cover in a graph is a set of vertices that includes at least one endpoint of every edge, and a vertex cover is ''minimum'' if no other vertex cover has fewer vertices. A matching in a graph is a set of edges no two of which share an endpoint, and a matching is ''maximum'' if no other matching has more edges. It is obvious from the definition that any vertex-cover set must be at least as large as any matching set (since for every edge in the matching, at least one vertex is needed in the cover). In particular, the minimum vertex cover set is at least as large as the maximum matching set. Kőnig's theorem states that, in any bipartite graph, the minimum vertex c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorial Optimization
Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the set of feasible solutions is discrete or can be reduced to a discrete set. Typical combinatorial optimization problems are the travelling salesman problem ("TSP"), the minimum spanning tree problem ("MST"), and the knapsack problem. In many such problems, such as the ones previously mentioned, exhaustive search is not tractable, and so specialized algorithms that quickly rule out large parts of the search space or approximation algorithms must be resorted to instead. Combinatorial optimization is related to operations research, algorithm theory, and computational complexity theory. It has important applications in several fields, including artificial intelligence, machine learning, auction theory, software engineering, VLSI, applied mathematics and theoretical computer science. Some research literature considers discrete o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
