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Auction Algorithm
The term "auction algorithm"Dimitri P. Bertsekas. "A distributed algorithm for the assignment problem"original paper, 1979 applies to several variations of a Optimization (mathematics), combinatorial optimization algorithm which solves assignment problems, and network optimization problems with linear and convex/nonlinear cost. An ''auction algorithm'' has been used in a business setting to determine the best prices on a set of products offered to multiple buyers. It is an iterative procedure, so the name "auction algorithm" is related to a sales auction, where multiple bids are compared to determine the best offer, with the final sales going to the highest bidders. The original form of the auction algorithm is an iterative method to find the optimal prices and an assignment that maximizes the net benefit in a bipartite graph, the ''maximum weight matching problem'' (MWM).M.G. Resende, P.M. Pardalos. "Handbook of optimization in telecommunications"2006/ref>M. Bayati, D. Shah, M. S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimitri P
Dimitri may refer People * Dmitry, a male given name, Slavic version of Greek name Demetrios * Dimitri (clown) (1935–2016), Swiss clown and mime * Dimitri Atanasescu, Ottoman-born Aromanian teacher * Dimitri from Paris, French DJ * Dimitri Flowers (born 1996), American football player * Dimitri Payet (born 1987), French footballer * Dimitri Roger (born 1992), American rapper known professionally as Rich the Kid * Dimitri Vegas, Belgian DJ, part of Dimitri Vegas & Like Mike Other * Dimitri (Joncières), ''Dimitri'' (Joncières), 1876 based on Schiller's ''Demetrius'' * Dimitrij (opera), ''Dimitrij'' (opera), Dvořák opera, 1881 also based on Schiller's ''Demetrius'' * Dimethyltryptamine, an endogenous and hallucinogenic tryptamine more commonly known as DMT * Dimitri, an early codename for the video game ''Milo and Kate'' by Lionhead Studios * Dimitri Alexandre Blaiddyd, a character from the video games ''Fire Emblem: Three Houses'' and ''Fire Emblem Warriors: Three Hopes'' * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimization (mathematics)
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a define ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a Heuristic (computer science), heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm ca ... [...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] |
Auction
An auction is usually a process of buying and selling goods or services by offering them up for bids, taking bids, and then selling the item to the highest bidder or buying the item from the lowest bidder. Some exceptions to this definition exist and are described in the section about different types. The branch of economic theory dealing with auction types and participants' behavior in auctions is called auction theory. The open ascending price auction is arguably the most common form of auction and has been used throughout history. Participants bid openly against one another, with each subsequent bid being higher than the previous bid. An auctioneer may announce prices, while bidders submit bids vocally or electronically. Auctions are applied for trade in diverse contexts. These contexts include antiques, paintings, rare collectibles, expensive wines, commodities, livestock, radio spectrum, used cars, real estate, online advertising, vacation packages, emission trading, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bipartite Graph
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets U and V, that is every edge connects a vertex in U to one in V. Vertex sets U and V are usually called the ''parts'' of the graph. Equivalently, a bipartite graph is a graph that does not contain any odd-length cycles. The two sets U and V may be thought of as a coloring of the graph with two colors: if one colors all nodes in U blue, and all nodes in V red, each edge has endpoints of differing colors, as is required in the graph coloring problem.. In contrast, such a coloring is impossible in the case of a non-bipartite graph, such as a triangle: after one node is colored blue and another red, the third vertex of the triangle is connected to vertices of both colors, preventing it from being assigned either color. One often writes G=(U,V,E) to denote a bipartite graph whose partition has the parts U and V, with E denoting ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Weight Matching
In computer science and graph theory, the maximum weight matching problem is the problem of finding, in a weighted graph, a matching in which the sum of weights is maximized. A special case of it is the assignment problem, in which the input is restricted to be a bipartite graph, and the matching constrained to be have cardinality that of the smaller of the two partitions. Another special case is the problem of finding a maximum cardinality matching on an unweighted graph: this corresponds to the case where all edge weights are the same. Algorithms There is a O(V^E) time algorithm to find a maximum matching or a maximum weight matching in a graph that is not bipartite; it is due to Jack Edmonds, is called the ''paths, trees, and flowers'' method or simply Edmonds' algorithm, and uses bidirected edges. A generalization of the same technique can also be used to find maximum independent set In graph theory, an independent set, stable set, coclique or anticlique is a set ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimitri Bertsekas
Dimitri Panteli Bertsekas (born 1942, Athens, el, Δημήτρης Παντελής Μπερτσεκάς) is an applied mathematician, electrical engineer, and computer scientist, a McAfee Professor at the Department of Electrical Engineering and Computer Science in School of Engineering at the Massachusetts Institute of Technology (MIT), Cambridge, Massachusetts, and also a Fulton Professor of Computational Decision Making at Arizona State University, Tempe. Biography Bertsekas was born in Greece and lived his childhood there. He studied for five years at the National Technical University of Athens, Greece and studied for about a year and a half at The George Washington University, Washington, D.C., where he obtained his M.S. in electrical engineering in 1969, and for about two years at MIT, where he obtained his doctorate in system science in 1971. Prior to joining the MIT faculty in 1979, he taught for three years at the Engineering-Economic Systems Dept. of Stanford Un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shortest Path Problem
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. The problem of finding the shortest path between two intersections on a road map may be modeled as a special case of the shortest path problem in graphs, where the vertices correspond to intersections and the edges correspond to road segments, each weighted by the length of the segment. Definition The shortest path problem can be defined for graphs whether undirected, directed, or mixed. It is defined here for undirected graphs; for directed graphs the definition of path requires that consecutive vertices be connected by an appropriate directed edge. Two vertices are adjacent when they are both incident to a common edge. A path in an undirected graph is a sequence of vertices P = ( v_1, v_2, \ldots, v_n ) \in V \times V \times \cdots \times V such that v_i is adjacent to v_ for 1 \leq i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Directed Graph
In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed edges, often called arcs. Definition In formal terms, a directed graph is an ordered pair where * ''V'' is a set whose elements are called '' vertices'', ''nodes'', or ''points''; * ''A'' is a set of ordered pairs of vertices, called ''arcs'', ''directed edges'' (sometimes simply ''edges'' with the corresponding set named ''E'' instead of ''A''), ''arrows'', or ''directed lines''. It differs from an ordinary or undirected graph, in that the latter is defined in terms of unordered pairs of vertices, which are usually called ''edges'', ''links'' or ''lines''. The aforementioned definition does not allow a directed graph to have multiple arrows with the same source and target nodes, but some authors consider a broader definition that allows directed graphs to have such multiple arcs (namely, they allow the arc set to be a m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotonic Function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus and analysis In calculus, a function f defined on a subset of the real numbers with real values is called ''monotonic'' if and only if it is either entirely non-increasing, or entirely non-decreasing. That is, as per Fig. 1, a function that increases monotonically does not exclusively have to increase, it simply must not decrease. A function is called ''monotonically increasing'' (also ''increasing'' or ''non-decreasing'') if for all x and y such that x \leq y one has f\!\left(x\right) \leq f\!\left(y\right), so f preserves the order (see Figure 1). Likewise, a function is called ''monotonically decreasing'' (also ''decreasing'' or ''non-increasing'') if, whenever x \leq y, then f\!\left(x\right) \geq f\!\left(y\ri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hungarian Algorithm
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] |
