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Traveling Tournament Problem
The traveling tournament problem (TTP) is a mathematical optimization problem. The question involves scheduling a series of teams such that: #Each team plays every other team twice, once at home and once in the other's stadium. #No team plays the same opponent in two consecutive weeks. #No team plays more than three games in a row at home, or three games in a row on the road. A matrix is provided of the travel distances between each team's home city. All teams start and end at their own home city, and the goal is to minimize the total travel distance for every team over the course of the whole season A season is a division of the year based on changes in weather, ecology, and the number of daylight hours in a given region. On Earth, seasons are the result of the axial parallelism of Earth's tilted orbit around the Sun. In temperate and pol .... There have been many papers published on the subject, and a contest exists to find the best solutions for certain specific schedules ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Optimization
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 maxima and minima, maximizing or minimizing a Function of a real variable, real function by systematically choosing Argument of a function, input values from within an allowed set and computing the Value (mathematics), value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, opti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sports Team
A sports team is a group of individuals who play sports (sports player), usually team sports, on the same team. The number of players in the group depends on type of the sports requirements. Historically, sports teams and the people who play sports have been amateur sports, amateurs. However, by the 20th century, some sports teams and their associated leagues became extremely valuable with net worth in the millions. The Dallas Cowboys are rated by Forbes as the world's Forbes' list of the most valuable sports teams, most valuable sports team at US$4.2 billion. Some individual sports have modified rules that allow them to be played by teams. Team identities can be formed from a number of sources, most often a type of geographic location, e.g., the Dallas Cowboys are named after Dallas, Texas, US. Some teams can also be named after an institution, such as the Alabama Crimson Tide, which are supported by and named after the University of Alabama, or the Yomiuri Giants, who are na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Round-robin Tournament
A round-robin tournament (or all-go-away-tournament) is a competition Competition is a rivalry where two or more parties strive for a common goal which cannot be shared: where one's gain is the other's loss (an example of which is a zero-sum game). Competition can arise between entities such as organisms, indiv ... in which each contestant meets every other participant, usually in turn.''Webster's Third New International Dictionary of the English Language, Unabridged'' (1971, G. & C. Merriam Co), p.1980. A round-robin contrasts with an elimination tournament, in which participants/teams are eliminated after a certain number of losses. Terminology The term ''round-robin'' is derived from the French term ''ruban'', meaning "ribbon". Over a long period of time, the term was Folk etymology, corrupted and idiomized to ''robin''. In a ''single round-robin'' schedule, each participant plays every other participant once. If each participant plays all others twice, this is freque ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Home Team
In sports, home is the place and venue identified with a team sport. Most professional teams are named for, and marketed to, particular metropolitan areas; amateur teams may be drawn from a particular region, or from institutions such as schools or universities. When they play in that venue, they are said to be the "home team"; when the team plays elsewhere, they are the ''away'', ''visiting'', or ''road'' team. Home teams wear home colors. Venue Each team has a location where it practices during the season and where it hosts games. This is referred to as the home court, home field, home stadium, home ballpark, home arena, home ground, or home ice. When a team is serving as host of a contest, it is designated as the "home team". The event is described as a "home game" for that team and the venue that the game is being played is described as the "home field." In most sports, there is a home field advantage whereby the home team wins more frequently because it has a greater ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Visiting Team
A road game or away game is a sports game where the specified team is not the host and must travel to another venue. Most professional teams represent cities or towns and amateur sports teams often represent academic institutions. Each team has a location where it practices during the season and where it hosts games. When a team is not the host, it must travel to games (usually by bus or car, hence "road", though increasingly also by plane for longer journeys). Thus, when a team is not hosting a game, the team is described as the road team, the visiting team, or the away team, and the game is described as a road game or an away game for that team. The venue in which the game is played is described as the visiting stadium or the road. The host team is said to be the home team. The home team is often thought to have a home advantage over the visiting team, because of their familiarity with the environment, their shorter travel times, and the influence that a parochial crowd ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix (mathematics)
In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, \begin1 & 9 & -13 \\20 & 5 & -6 \end is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a "-matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra. Therefore, the study of matrices is a large part of linear algebra, and most properties and operations of abstract linear algebra can be expressed in terms of matrices. For example, matrix multiplication represents composition of linear maps. Not all matrices are related to linear algebra. This is, in particular, the case in graph theory, of incidence matrices, and adjacency matrices. ''This article focuses on matrices related to linear algebra, and, unle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Season (sports)
In an organized sports league, a typical season is the portion of one year in which regulated games of the sport are in session: for example, in Major League Baseball the season lasts approximately from the last week of March to the last week of September. In other team sports, like association football or basketball, it is generally from August or September to May although in some countries - such as Northern Europe or East Asia - the season starts in the spring and finishes in autumn, mainly due to weather conditions encountered during the winter. A year can often be broken up into several distinct sections (sometimes themselves called seasons). These are: a preseason, a series of exhibition games played for training purposes; a regular season, the main period of the league's competition; the postseason, a playoff tournament played against the league's top teams to determine the league's champion; and the offseason, the time when there is no official competition. Preseason In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Problems
A mathematical problem is a problem that can be represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert's problems. It can also be a problem referring to the nature of mathematics itself, such as Russell's Paradox. Real-world problems Informal "real-world" mathematical problems are questions related to a concrete setting, such as "Adam has five apples and gives John three. How many has he left?". Such questions are usually more difficult to solve than regular mathematical exercises like "5 − 3", even if one knows the mathematics required to solve the problem. Known as word problems, they are used in mathematics education to teach students to connect real-world situations to the abstract language of mathematics. In general, to use mathematics for solving a real-world problem, the first ste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
