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19 relations: Approximation algorithm, APX, Bipartite graph, Computational complexity theory, Decision problem, Dover Publications, Exact cover, Graph theory, Hopcroft–Karp algorithm, Hypergraph, Karp's 21 NP-complete problems, List of NP-complete problems, Matching (graph theory), Mathematics, NP-completeness, NP-hardness, Optimization problem, Set packing, Springer Science+Business Media.
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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APX
In complexity theory the class APX (an abbreviation of "approximable") is the set of NP optimization problems that allow polynomial-time approximation algorithms with approximation ratio bounded by a constant (or constant-factor approximation algorithms for short).
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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 such that every edge connects a vertex in U to one in V. Vertex sets U and V are usually called the parts of the graph.
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Computational complexity theory
Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.
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Decision problem
In computability theory and computational complexity theory, a decision problem is a problem that can be posed as a yes-no question of the input values.
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Dover Publications
Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward Cirker and his wife, Blanche.
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Exact cover
In mathematics, given a collection \mathcal of subsets of a set X, an exact cover is a subcollection \mathcal^* of \mathcal such that each element in X is contained in exactly one subset in \mathcal^*.
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Graph theory
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
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Hopcroft–Karp algorithm
In computer science, the Hopcroft–Karp algorithm is an algorithm that takes as input a bipartite graph and produces as output a maximum cardinality matching – a set of as many edges as possible with the property that no two edges share an endpoint.
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Hypergraph
In mathematics, a hypergraph is a generalization of a graph in which an edge can join any number of vertices.
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Karp's 21 NP-complete problems
In computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete.
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List of NP-complete problems
This is a list of some of the more commonly known problems that are NP-complete when expressed as decision problems.
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Matching (graph theory)
In the mathematical discipline of graph theory, a matching or independent edge set in a graph is a set of edges without common vertices.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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NP-completeness
In computational complexity theory, an NP-complete decision problem is one belonging to both the NP and the NP-hard complexity classes.
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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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Optimization problem
In mathematics and computer science, an optimization problem is the problem of finding the best solution from all feasible solutions.
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Set packing
Set packing is a classical NP-complete problem in computational complexity theory and combinatorics, and was one of Karp's 21 NP-complete problems.
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Springer Science+Business Media
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
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