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Jack R. Edmonds
Jack R. Edmonds (born April 5, 1934) is an American-born and educated computer scientist and mathematician who lived and worked in Canada for much of his life. He has made fundamental contributions to the fields of combinatorial optimization, polyhedral combinatorics, discrete mathematics and the theory of computing. He was the recipient of the 1985 John von Neumann Theory Prize. Early career Edmonds attended McKinley Technology High School, graduating in 1952; and has talked about the influence this school had on his career (for instance at his 2014 NIST Gallery induction ). Edmonds attended Duke University before completing his undergraduate degree at George Washington University in 1957. He thereafter received a master's degree in 1960 at the University of Maryland under Bruce L. Reinhart with a thesis on the problem of embedding graphs into surfaces. From 1959 to 1969 he worked at the National Institute of Standards and Technology (then the National Bureau of Standards), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polymatroid
In mathematics, a polymatroid is a polytope associated with a submodular function. The notion was introduced by Jack Edmonds in 1970. It is also a generalization of the notion of a matroid. Definition Polyhedral definition Let E be a finite set and f: 2^E\rightarrow \mathbb_ a non-decreasing submodular function, that is, for each A\subseteq B \subseteq E we have f(A)\leq f(B) , and for each A, B \subseteq E we have f(A)+f(B) \geq f(A\cup B) + f(A\cap B) . We define the polymatroid associated to f to be the following polytope: P_f= \Big\. When we allow the entries of \textbf to be negative we denote this polytope by EP_f, and call it the extended polymatroid associated to f. Matroidal definition In matroid theory, polymatroids are defined as the pair consisting of the set and the function as in the above definition. That is, a polymatroid is a pair (E, f) where E is a finite set and f:2^E\rightarrow \mathbb_, or \mathbb_, is a non-decreasing submodular function. If the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Matching
Maximum cardinality matching is a fundamental problem in graph theory. We are given a graph , and the goal is to find a matching containing as many edges as possible; that is, a maximum cardinality subset of the edges such that each vertex is adjacent to at most one edge of the subset. As each edge will cover exactly two vertices, this problem is equivalent to the task of finding a matching that covers as many vertices as possible. An important special case of the maximum cardinality matching problem is when is a bipartite graph, whose vertices are partitioned between left vertices in and right vertices in , and edges in always connect a left vertex to a right vertex. In this case, the problem can be efficiently solved with simpler algorithms than in the general case. Algorithms for bipartite graphs Flow-based algorithm The simplest way to compute a maximum cardinality matching is to follow the Ford–Fulkerson algorithm. This algorithm solves the more general problem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blossom Algorithm
In graph theory, the blossom algorithm is an algorithm for constructing maximum matchings on Graph (discrete mathematics), graphs. The algorithm was developed by Jack Edmonds in 1961, and published in 1965. Given a general Graph (discrete mathematics), graph , the algorithm finds a matching such that each vertex in is incident with at most one edge in and is maximized. The matching is constructed by iteratively improving an initial empty matching along augmenting paths in the graph. Unlike bipartite graph, bipartite matching, the key new idea is that an odd-length cycle in the graph (blossom) is contracted to a single vertex, with the search continuing iteratively in the contracted graph. The algorithm runs in time , where is the number of edge (graph), edges of the graph and is its number of vertex (graph), vertices. A better running time of O( , E, \sqrt ) for the same task can be achieved with the much more complex algorithm of Micali and Vazirani. A major reason that t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RAND Corporation
The RAND Corporation, doing business as RAND, is an American nonprofit global policy think tank, research institute, and public sector consulting firm. RAND engages in research and development (R&D) in several fields and industries. Since the 1950s, RAND research has helped inform United States policy decisions on a wide variety of issues, including the Cold War space race, the U.S. involvement in the Vietnam War, the U.S.–Soviet nuclear arms confrontation, the creation of the Great Society social welfare programs, and national health care. RAND originated as "Project RAND" (from the phrase "research and development") in the post-war period immediately after World War II. The U.S. Army Air Forces established Project RAND with the objective of investigating long-range planning of future weapons. Douglas Aircraft Company was granted a contract to research intercontinental warfare. Project RAND later evolved into RAND, and expanded its research into civilian fields suc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alan J
Alan may refer to: People *Alan (surname), an English and Kurdish surname * Alan (given name), an English given name ** List of people with given name Alan ''Following are people commonly referred to solely by "Alan" or by a homonymous name.'' * Alan (Chinese singer) (born 1987), female Chinese singer of Tibetan ethnicity, active in both China and Japan * Alan (Mexican singer) (born 1973), Mexican singer and actor * Alan (wrestler) (born 1975), a.k.a. Gato Eveready, who wrestles in Asistencia Asesoría y Administración * Alan (footballer, born 1979) (Alan Osório da Costa Silva), Brazilian footballer * Alan (footballer, born 1998) (Alan Cardoso de Andrade), Brazilian footballer * Alan I, King of Brittany (died 907), "the Great" * Alan II, Duke of Brittany (c. 900–952) * Alan III, Duke of Brittany(997–1040) * Alan IV, Duke of Brittany (c. 1063–1119), a.k.a. Alan Fergant ("the Younger" in Breton language) * Alan of Tewkesbury, 12th century abbott * Alan of Lynn (c. 1348–142 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
McKinley Technology High School
McKinley Technology High School is a public citywide 9th–12th grade high school in the District of Columbia Public Schools in Northeast Washington, D.C. The school, an offshoot of Central High School (now Cardozo Senior High School), originally was called McKinley Technical High School and was located at 7th Street NW and Rhode Island Avenue NW in the District of Columbia. The United States Congress allocated $26 million in 1926 for the construction of the existing building at 2nd and T Streets NE, in the Eckington area. The school is named for William McKinley, the 25th president of the United States. Academics McKinley Tech is a STEM-focused DCPS application high school. Students focus on one of three courses of study: Engineering, Information Technology (Networking, Computer Science, and Digital Media), or Biotechnology. History The school was exclusively for white residents of the City of Washington until integrated with other DC schools by an Executive Order by Pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Mathematics
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions). Objects studied in discrete mathematics include integers, Graph (discrete mathematics), graphs, and Statement (logic), statements in Mathematical logic, logic. By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumeration, enumerated by integers; more formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets (finite sets or sets with the same cardinality as the natural numbers). However, there is no exact definition of the term "discrete mathematics". The set of objects studied in discrete mathematics can be finite or infinite. The term finite mathematics is sometime ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyhedral Combinatorics
Polyhedral combinatorics is a branch of mathematics, within combinatorics and discrete geometry, that studies the problems of counting and describing the faces of convex polyhedra and higher-dimensional convex polytopes. Research in polyhedral combinatorics falls into two distinct areas. Mathematicians in this area study the combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ... of polytopes; for instance, they seek inequality (mathematics), inequalities that describe the relations between the numbers of vertex (geometry), vertices, edge (geometry), edges, and faces of higher dimensions in arbitrary polytopes or in certain important subclasses of polytopes, and study other combinatorial properties of polytopes such as their Connectivity (graph theory), connectivity and dia ... [...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. Applications Basic applications of combina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Scientist
A computer scientist is a scientist who specializes in the academic study of computer science. Computer scientists typically work on the theoretical side of computation. Although computer scientists can also focus their work and research on specific areas (such as algorithm and data structure development and design, software engineering, information theory, database theory, theoretical computer science, numerical analysis, programming language theory, compiler, computer graphics, computer vision, robotics, computer architecture, operating system), their foundation is the theoretical study of computing from which these other fields derive. A primary goal of computer scientists is to develop or validate models, often mathematical, to describe the properties of computational systems (Processor (computing), processors, programs, computers interacting with people, computers interacting with other computers, etc.) with an overall objective of discovering designs that yield useful ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
