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Index NP-completeness

In computational complexity theory, an NP-complete decision problem is one belonging to both the NP and the NP-hard complexity classes. [1]

107 relations: Abstract machine, AC0, Academic Press, ACM SIGACT, Advanced Encryption Standard, Alfred Aho, Algorithm, Approximation algorithm, Bipartite graph, Boolean satisfiability problem, Charles E. Leiserson, Clay Mathematics Institute, Clifford Stein, Clique problem, Co-NP, Co-NP-complete, Communications of the ACM, Complement (complexity), Computational complexity theory, Computer scientist, Computers and Intractability, Concatenation, Cook–Levin theorem, Cycle graph, David S. Johnson, Decision problem, Determinism, Dominating set, Donald Knuth, Gadget (computer science), Galley proof, Genetic algorithm, Gerhard J. Woeginger, Graph coloring, Graph isomorphism, Graph isomorphism problem, Graph theory, Greedy coloring, Hamiltonian path problem, Heuristic (computer science), Independent set (graph theory), Intersection, Introduction to Algorithms, Isomorphism, Jeffrey Ullman, John Hopcroft, Karp's 21 NP-complete problems, Kenneth Steiglitz, Kleene star, Knapsack problem, ..., L (complexity), Labours of Hercules, Lance Fortnow, List of NP-complete problems, List of unsolved problems in computer science, List of unsolved problems in mathematics, Log-space reduction, Many-one reduction, Marek Karpinski, Metaheuristic, Michael Garey, Minimum spanning tree, Monte Carlo method, National Central University, National Tsing Hua University, NL-complete, Non-deterministic Turing machine, NP (complexity), NP-hardness, NP-intermediate, Open problem, P (complexity), P versus NP problem, P-complete, Parameterized complexity, Planar graph, Planar separator theorem, Polynomial-time reduction, Presburger arithmetic, Programmer, Randomized algorithm, Reduced instruction set computer, Reduction (complexity), Register allocation, Resource bounded measure, Richard M. Karp, Ron Rivest, Scott Aaronson, SIAM Journal on Computing, Stanford University, Strong NP-completeness, Subgraph isomorphism problem, Subset sum problem, Symposium on Theory of Computing, Theoretical computer science, Time complexity, Travelling salesman problem, Turing completeness, Turing machine, Union (set theory), Universal Turing machine, University of Liverpool, Valiant–Vazirani theorem, Vertex (graph theory), Vertex cover, Victor Klee, 2-satisfiability. Expand index (57 more) »

Abstract machine

An abstract machine, also called an abstract computer, is a theoretical model of a computer hardware or software system used in automata theory.

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AC0 is a complexity class used in circuit complexity.

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Academic Press

Academic Press is an academic book publisher.

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ACM SIGACT or SIGACT is the Association for Computing Machinery Special Interest Group on Algorithms and Computation Theory, whose purpose is support of research in theoretical computer science.

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Advanced Encryption Standard

The Advanced Encryption Standard (AES), also known by its original name Rijndael, is a specification for the encryption of electronic data established by the U.S. National Institute of Standards and Technology (NIST) in 2001.

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Alfred Aho

Alfred Vaino Aho (born August 9, 1941) is a Canadian computer scientist best known for his work on programming languages, compilers, and related algorithms, and his textbooks on the art and science of computer programming.

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In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.

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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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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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Boolean satisfiability problem

In computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated as SATISFIABILITY or SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula.

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Charles E. Leiserson

Charles Eric Leiserson is a computer scientist, specializing in the theory of parallel computing and distributed computing, and particularly practical applications thereof.

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Clay Mathematics Institute

The Clay Mathematics Institute (CMI) is a private, non-profit foundation, based in Peterborough, New Hampshire, United States.

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Clifford Stein

Clifford Seth Stein (born December 14, 1965), a computer scientist, is a professor of industrial engineering and operations research at Columbia University in New York, NY, where he also holds an appointment in the Department of Computer Science.

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Clique problem

In computer science, the clique problem is the computational problem of finding cliques (subsets of vertices, all adjacent to each other, also called complete subgraphs) in a graph.

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In computational complexity theory, co-NP is a complexity class.

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In complexity theory, computational problems that are co-NP-complete are those that are the hardest problems in co-NP, in the sense that any problem in co-NP can be reformulated as a special case of any co-NP-complete problem with only polynomial overhead.

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Communications of the ACM

Communications of the ACM is the monthly journal of the Association for Computing Machinery (ACM).

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Complement (complexity)

In computational complexity theory, the complement of a decision problem is the decision problem resulting from reversing the yes and no answers.

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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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Computer scientist

A computer scientist is a person who has acquired the knowledge of computer science, the study of the theoretical foundations of information and computation and their application.

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Computers and Intractability

In computer science, more specifically computational complexity theory, Computers and Intractability: A Guide to the Theory of NP-Completeness is an influential textbook by Michael Garey and David S. Johnson.

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In formal language theory and computer programming, string concatenation is the operation of joining character strings end-to-end.

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Cook–Levin theorem

In computational complexity theory, the Cook–Levin theorem, also known as Cook's theorem, states that the Boolean satisfiability problem is NP-complete.

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Cycle graph

In graph theory, a cycle graph or circular graph is a graph that consists of a single cycle, or in other words, some number of vertices connected in a closed chain.

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David S. Johnson

David Stifler Johnson (December 9, 1945 – March 8, 2016) was an American computer scientist specializing in algorithms and optimization.

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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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Determinism is the philosophical theory that all events, including moral choices, are completely determined by previously existing causes.

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Dominating set

In graph theory, a dominating set for a graph G.

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Donald Knuth

Donald Ervin Knuth (born January 10, 1938) is an American computer scientist, mathematician, and professor emeritus at Stanford University.

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Gadget (computer science)

In computational complexity theory, a gadget is a subset of a problem instance that simulates the behavior of one of the fundamental units of a different computational problem.

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Galley proof

In printing and publishing, proofs are the preliminary versions of publications meant for review by authors, editors, and proofreaders, often with extra-wide margins.

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Genetic algorithm

In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA).

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Gerhard J. Woeginger

Gerhard J. Woeginger is an Austrian mathematician and computer scientist who works in Germany as a professor at RWTH Aachen University, where he chairs the algorithms and complexity group in the department of computer science.

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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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Graph isomorphism

In graph theory, an isomorphism of graphs G and H is a bijection between the vertex sets of G and H such that any two vertices u and v of G are adjacent in G if and only if ƒ(u) and ƒ(v) are adjacent in H. This kind of bijection is commonly described as "edge-preserving bijection", in accordance with the general notion of isomorphism being a structure-preserving bijection.

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Graph isomorphism problem

The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic.

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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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Greedy coloring

In the study of graph coloring problems in mathematics and computer science, a greedy coloring is a coloring of the vertices of a graph formed by a greedy algorithm that considers the vertices of the graph in sequence and assigns each vertex its first available color.

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Hamiltonian path problem

In the mathematical field of graph theory the Hamiltonian path problem and the Hamiltonian cycle problem are problems of determining whether a Hamiltonian path (a path in an undirected or directed graph that visits each vertex exactly once) or a Hamiltonian cycle exists in a given graph (whether directed or undirected).

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Heuristic (computer science)

In computer science, artificial intelligence, and mathematical optimization, a heuristic (from Greek εὑρίσκω "I find, discover") is a technique designed for solving a problem more quickly when classic methods are too slow, or for finding an approximate solution when classic methods fail to find any exact solution.

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Independent set (graph theory)

In graph theory, an independent set or stable set is a set of vertices in a graph, no two of which are adjacent.

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In mathematics, the intersection of two or more objects is another, usually "smaller" object.

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Introduction to Algorithms

Introduction to Algorithms is a book by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein.

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In mathematics, an isomorphism (from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism or morphism (i.e. a mathematical mapping) that can be reversed by an inverse morphism.

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Jeffrey Ullman

Jeffrey David "Jeff" Ullman (born November 22, 1942) is an American computer scientist and professor at Stanford University.

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John Hopcroft

John Edward Hopcroft (born October 7, 1939) is an American theoretical computer scientist.

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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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Kenneth Steiglitz


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Kleene star

In mathematical logic and computer science, the Kleene star (or Kleene operator or Kleene closure) is a unary operation, either on sets of strings or on sets of symbols or characters.

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Knapsack problem

The knapsack problem or rucksack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.

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L (complexity)

In computational complexity theory, L (also known as LSPACE or DLOGSPACE) is the complexity class containing decision problems that can be solved by a deterministic Turing machine using a logarithmic amount of writable memory space.

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Labours of Hercules

--> The Twelve Labours of Heracles or of Hercules (ἆθλοι, hoi Hērakleous athloi) are a series of episodes concerning a penance carried out by Heracles, the greatest of the Greek heroes, whose name was later Romanised as Hercules.

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Lance Fortnow

Lance Jeremy Fortnow (born August 15, 1963) is a computer scientist known for major results in computational complexity and interactive proof systems.

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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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List of unsolved problems in computer science

This article is a list of unsolved problems in computer science.

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List of unsolved problems in mathematics

Since the Renaissance, every century has seen the solution of more mathematical problems than the century before, and yet many mathematical problems, both major and minor, still remain unsolved.

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Log-space reduction

In computational complexity theory, a log-space reduction is a reduction computable by a deterministic Turing machine using logarithmic space.

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Many-one reduction

In computability theory and computational complexity theory, a many-one reduction is a reduction which converts instances of one decision problem into instances of a second decision problem.

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Marek Karpinski

Marek Karpinski is a computer scientist and mathematician known for his research in the theory of algorithms and their applications, combinatorial optimization, computational complexity, and mathematical foundations.

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In computer science and mathematical optimization, a metaheuristic is a higher-level procedure or heuristic designed to find, generate, or select a heuristic (partial search algorithm) that may provide a sufficiently good solution to an optimization problem, especially with incomplete or imperfect information or limited computation capacity.

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Michael Garey

Michael Randolph Garey is a computer science researcher, and co-author (with David S. Johnson) of Computers and Intractability: A Guide to the Theory of NP-completeness.

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Minimum spanning tree

A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted (un)directed graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight.

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Monte Carlo method

Monte Carlo methods (or Monte Carlo experiments) are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results.

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National Central University

National Central University (NCU,, Kuo-Li Chung-yang Ta-hsüeh, or 中大, Chung-ta) was founded in 1915 with roots from 258 CE in mainland China.

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National Tsing Hua University

National Tsing Hua University (NTHU) is a research university located in Hsinchu City, Republic of China (Taiwan).

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In computational complexity theory, NL-complete is a complexity class containing the languages that are complete for NL, the class of decision problems that can be solved by a nondeterministic Turing machine using a logarithmic amount of memory space.

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Non-deterministic Turing machine

In theoretical computer science, a Turing machine is a theoretical machine that is used in thought experiments to examine the abilities and limitations of computers.

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NP (complexity)

In computational complexity theory, NP (for nondeterministic polynomial time) is a complexity class used to describe certain types of decision problems.

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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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In computational complexity, problems that are in the complexity class NP but are neither in the class P nor NP-complete are called NP-intermediate, and the class of such problems is called NPI.

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Open problem

In science and mathematics, an open problem or an open question is a known problem which can be accurately stated, and which is assumed to have an objective and verifiable solution, but which has not yet been solved (no solution for it is known).

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P (complexity)

In computational complexity theory, P, also known as PTIME or DTIME(nO(1)), is a fundamental complexity class.

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P versus NP problem

The P versus NP problem is a major unsolved problem in computer science.

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In complexity theory, a decision problem is P-complete (complete for the complexity class '''P''') if it is in P and every problem in P can be reduced to it by an appropriate reduction.

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Parameterized complexity

In computer science, parameterized complexity is a branch of computational complexity theory that focuses on classifying computational problems according to their inherent difficulty with respect to multiple parameters of the input or output.

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Planar graph

In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints.

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Planar separator theorem

In graph theory, the planar separator theorem is a form of isoperimetric inequality for planar graphs, that states that any planar graph can be split into smaller pieces by removing a small number of vertices.

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Polynomial-time reduction

In computational complexity theory, a polynomial-time reduction is a method of solving one problem by means of a hypothetical subroutine for solving a different problem (that is, a reduction), that uses polynomial time excluding the time within the subroutine.

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Presburger arithmetic

Presburger arithmetic is the first-order theory of the natural numbers with addition, named in honor of Mojżesz Presburger, who introduced it in 1929.

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A programmer, developer, dev, coder, or software engineer is a person who creates computer software.

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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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Reduced instruction set computer

A reduced instruction set computer, or RISC (pronounced 'risk'), is one whose instruction set architecture (ISA) allows it to have fewer cycles per instruction (CPI) than a complex instruction set computer (CISC).

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Reduction (complexity)

In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem.

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Register allocation

In compiler optimization, register allocation is the process of assigning a large number of target program variables onto a small number of CPU registers.

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Resource bounded measure

Lutz's resource bounded measure is a generalisation of Lebesgue measure to complexity classes.

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Richard M. Karp

Richard Manning Karp (born January 3, 1935) is an American computer scientist and computational theorist at the University of California, Berkeley.

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Ron Rivest

Ronald Linn Rivest (born May 6, 1947) is a cryptographer and an Institute Professor at MIT.

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Scott Aaronson

Scott Joel Aaronson (born May 21, 1981) is an American theoretical computer scientist and David J. Bruton Jr.

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SIAM Journal on Computing

The SIAM Journal on Computing is a scientific journal focusing on the mathematical and formal aspects of computer science.

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Stanford University

Stanford University (officially Leland Stanford Junior University, colloquially the Farm) is a private research university in Stanford, California.

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Strong NP-completeness

In computational complexity, strong NP-completeness is a property of computational problems that is a special case of NP-completeness.

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Subgraph isomorphism problem

In theoretical computer science, the subgraph isomorphism problem is a computational task in which two graphs G and H are given as input, and one must determine whether G contains a subgraph that is isomorphic to H. Subgraph isomorphism is a generalization of both the maximum clique problem and the problem of testing whether a graph contains a Hamiltonian cycle, and is therefore NP-complete.

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Subset sum problem

In computer science, the subset sum problem is an important problem in complexity theory and cryptography.

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Symposium on Theory of Computing

The Annual ACM Symposium on Theory of Computing (STOC) is an academic conference in the field of theoretical computer science.

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Theoretical computer science

Theoretical computer science, or TCS, is a subset of general computer science and mathematics that focuses on more mathematical topics of computing and includes the theory of computation.

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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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Turing completeness

In computability theory, a system of data-manipulation rules (such as a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing complete or computationally universal if it can be used to simulate any Turing machine.

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Turing machine

A Turing machine is a mathematical model of computation that defines an abstract machine, which manipulates symbols on a strip of tape according to a table of rules.

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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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Universal Turing machine

In computer science, a universal Turing machine (UTM) is a Turing machine that can simulate an arbitrary Turing machine on arbitrary input.

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University of Liverpool

The University of Liverpool is a public university based in the city of Liverpool, England.

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Valiant–Vazirani theorem

The Valiant–Vazirani theorem is a theorem in computational complexity theory stating that if there is a polynomial time algorithm for Unambiguous-SAT, then NP.

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Vertex (graph theory)

In mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices).

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Vertex cover

In the mathematical discipline of graph theory, a vertex cover (sometimes node cover) of a graph is a set of vertices such that each edge of the graph is incident to at least one vertex of the set.

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Victor Klee

Victor L. Klee, Jr. (September 18, 1925, San Francisco – August 17, 2007, Lakewood, Ohio) was a mathematician specialising in convex sets, functional analysis, analysis of algorithms, optimization, and combinatorics.

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In computer science, 2-satisfiability, 2-SAT or just 2SAT is a computational problem of assigning values to variables, each of which has two possible values, in order to satisfy a system of constraints on pairs of variables.

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Redirects here:

NP complete, NP completeness, NP-C, NP-Complete, NP-Completeness, NP-complete, NP-complete language, NP-complete problem, NP-complete problems, NP-incomplete, Non polynomial complete, Non-deterministic polynomial-time complete, Nondeterministic Polynomial Complete, Np complete, Np completeness, Np-Complete, Np-complete, Np-complete problem.


[1] https://en.wikipedia.org/wiki/NP-completeness

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