The Steiner tree problem, or the minimum Steiner tree problem, named after Jakob Steiner, is a problem in combinatorial optimization, which may be formulated in a number of settings, with the common part being that it is required to find the shortest interconnect for a given set of objects.
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Facility location
Facility location, also known as location analysis, is a branch of operations research and computational geometry concerning itself with mathematical modeling and solution of problems concerning optimal placement of facilities in order to minimize transportation costs, avoid placing hazardous materials near housing, outperform competitors' facilities, etc.
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Approximation algorithm
In computer science and operations research, approximation algorithms are algorithms used to find approximate solutions to optimization problems. Approximation algorithms are often associated with NP-hard problems; since it is unlikely that there can ever be efficient polynomial time exact algorithms solving NP-hard problems, one settles for polynomial time sub-optimal solutions.
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Combinatorial optimization
In applied mathematics and theoretical computer science, combinatorial optimization is a topic that consists of finding an optimal object from a finite set of objects. In many such problems, exhaustive search is not feasible. It operates on the domain of those optimization problems, in which the set of feasible solutions is discrete or can be reduced to discrete, and in which the goal is to find the best solution.
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Set cover problem
The set covering problem (SCP) is a classical question in computer science and complexity theory. It is a problem "whose study has led to the development of fundamental techniques for the entire field" of approximation algorithms. It was also one of Karp's 21 NP-complete problems shown to be NP-complete in 1972.
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Discrete optimization
Discrete optimization is a branch of optimization in applied mathematics and computer science. As opposed to continuous optimization, the variables used in the mathematical program (or some of them) are restricted to assume only discrete values, such as the integers.
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Hardness of approximation
In computer science, hardness of approximation is a field that studies the algorithmic complexity of finding near-optimal solutions to optimization problems. It complements the study of approximation algorithms by proving, for certain problems, a limit on the factors with which their solution can be efficiently approximated.
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Median
In statistics and probability theory, median is described as the numerical value separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle one. If there is an even number of observations, then there is no single middle value; the median is then usually defined to be the mean of the two middle values.
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