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26 relations: Approximation algorithm, Branch and bound, Branch and cut, Bulletin of the American Mathematical Society, Convex hull, Convex polytope, Cutting-plane method, Dummy variable (statistics), Facet (geometry), Fractional coloring, Graph coloring, Greedy algorithm, Harmonic number, Linear programming, Method of conditional probabilities, NP-hardness, Polyhedral combinatorics, Randomized algorithm, Randomized rounding, Relaxation (approximation), Set (mathematics), Set cover problem, Time complexity, Travelling salesman problem, Unimodular matrix, Union (set theory).
Approximation algorithm
In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to NP-hard optimization problems with provable guarantees on the distance of the returned solution to the optimal one.
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Branch and bound
Branch and bound (BB, B&B, or BnB) is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization.
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Branch and cut
Branch and cut is a method of combinatorial optimization for solving integer linear programs (ILPs), that is, linear programming (LP) problems where some or all the unknowns are restricted to integer values.
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Bulletin of the American Mathematical Society
The Bulletin of the American Mathematical Society is a quarterly mathematical journal published by the American Mathematical Society.
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Convex hull
In mathematics, the convex hull or convex envelope or convex closure of a set X of points in the Euclidean plane or in a Euclidean space (or, more generally, in an affine space over the reals) is the smallest convex set that contains X. For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around X., p. 3.
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Convex polytope
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn.
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Cutting-plane method
In mathematical optimization, the cutting-plane method is any of a variety of optimization methods that iteratively refine a feasible set or objective function by means of linear inequalities, termed cuts.
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Dummy variable (statistics)
In statistics and econometrics, particularly in regression analysis, a dummy variable (also known as an indicator variable, design variable, Boolean indicator, binary variable, or qualitative variable) is one that takes the value 0 or 1 to indicate the absence or presence of some categorical effect that may be expected to shift the outcome.
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Facet (geometry)
In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.
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Fractional coloring
Fractional coloring is a topic in a young branch of graph theory known as fractional graph theory.
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Graph coloring
In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints.
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Greedy algorithm
A greedy algorithm is an algorithmic paradigm that follows the problem solving heuristic of making the locally optimal choice at each stage with the intent of finding a global optimum.
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Harmonic number
In mathematics, the -th harmonic number is the sum of the reciprocals of the first natural numbers: Harmonic numbers are related to the harmonic mean in that the -th harmonic number is also times the reciprocal of the harmonic mean of the first positive integers.
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Linear programming
Linear programming (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.
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Method of conditional probabilities
In mathematics and computer science, the probabilistic method is used to prove the existence of mathematical objects with desired combinatorial properties.
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NP-hardness
NP-hardness (''n''on-deterministic ''p''olynomial-time hardness), in computational complexity theory, is the defining property of a class of problems that are, informally, "at least as hard as the hardest problems in NP".
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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.
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Randomized algorithm
A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic.
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Randomized rounding
Within computer science and operations research, many combinatorial optimization problems are computationally intractable to solve exactly (to optimality).
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Relaxation (approximation)
In mathematical optimization and related fields, relaxation is a modeling strategy.
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Set (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
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Set cover problem
The set cover problem is a classical question in combinatorics, computer science and complexity theory.
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Time complexity
In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.
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Travelling salesman problem
The travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in operations research and theoretical computer science.
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Unimodular matrix
In mathematics, a unimodular matrix M is a square integer matrix having determinant +1 or −1.
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Union (set theory)
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection.
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Integrality gap, LP relaxation, LP-relaxation.
References
[1] https://en.wikipedia.org/wiki/Linear_programming_relaxation
