computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete. In his 1972 paper, "Reducibility...
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the more commonly known problems that are NP-complete when expressed as decision problems. As there are thousands of such problems known, this list is in...
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NP-complete problems are the hardest of the problems to which solutions can be verified quickly. Somewhat more precisely, a problem is NP-complete when:...
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defined (Karp's 21 NP-complete problems, among the first found, were all well-known existing problems at the time they were shown to be NP-complete). Furthermore...
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Vertex cover (redirect from Vertex cover problem)
an NP-hard optimization problem that has an approximation algorithm. Its decision version, the vertex cover problem, was one of Karp's 21 NP-complete problems...
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Intractability: A Guide to the Theory of NP-Completeness and Richard Karp's list of 21 NP-complete problems. The problems of finding a Hamiltonian path and a...
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knapsack problem is often used to refer specifically to the subset sum problem. The subset sum problem is one of Karp's 21 NP-complete problems. Knapsack...
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Integer programming (redirect from Integer Programming Problem)
one of Karp's 21 NP-complete problems. If some decision variables are not discrete, the problem is known as a mixed-integer programming problem. In integer...
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polynomial. 3-SAT is one of Karp's 21 NP-complete problems, and it is used as a starting point for proving that other problems are also NP-hard. This is done by...
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covering is NP-complete. It is one of Karp's 21 NP-complete problems shown to be NP-complete in 1972. The optimization/search version of set cover is NP-hard...
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Exact cover (redirect from Exact cover problem)
problem to determine if an exact cover exists. The exact cover problem is NP-complete and is one of Karp's 21 NP-complete problems. It is NP-complete...
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In fact, the decision variant was among Karp's original 21 NP-complete problems. The Steiner tree problem in graphs has applications in circuit layout...
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Polynomial-time reduction (redirect from Karp reduction)
isomorphism problem itself is GI-complete, as are several other related problems. Karp's 21 NP-complete problems MIT OpenCourseWare: 16. Complexity: P, NP, NP-completeness...
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problem are hard. The clique decision problem is NP-complete (one of Karp's 21 NP-complete problems). The problem of finding the maximum clique is both...
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graph has a tour whose length is at most L) belongs to the class of NP-complete problems. Thus, it is possible that the worst-case running time for any algorithm...
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Graph coloring (redirect from Graph colouring problems)
algorithmic problem since the early 1970s: the chromatic number problem (see section § Vertex coloring below) is one of Karp's 21 NP-complete problems from 1972...
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Problems", in which he proved 21 problems to be NP-complete. In 1973 he and John Hopcroft published the Hopcroft–Karp algorithm, the fastest known method...
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Set packing (category NP-complete problems)
is a classical NP-complete problem in computational complexity theory and combinatorics, and was one of Karp's 21 NP-complete problems. Suppose one has...
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3-dimensional matching (category NP-complete problems)
This decision problem is known to be NP-complete; it is one of Karp's 21 NP-complete problems. It is NP-complete even in the special case that k = |X| = |Y| = |Z|...
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the maximum clique problem and the problem of testing whether a graph contains a Hamiltonian cycle, and is therefore NP-complete. However certain other...
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maximum clique, or all cliques, in a given graph. It is NP-complete, one of Karp's 21 NP-complete problems. It is also fixed-parameter intractable, and hard...
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Dominating set (redirect from Dominating set problem)
was one of Karp's 21 NP-complete problems. There exist a pair of polynomial-time L-reductions between the minimum dominating set problem and the set...
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Feedback arc set (redirect from Feedback arc set problem)
algorithms. It was one of Richard M. Karp's original set of 21 NP-complete problems; its NP-completeness was proved by Karp and Eugene Lawler by showing that...
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Cut (graph theory) (redirect from Sparsest cut problem)
cut is computationally hard. The max-cut problem is one of Karp's 21 NP-complete problems. The max-cut problem is also APX-hard, meaning that there is...
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Combinatorial optimization (redirect from NP optimization problem)
circulations, spanning trees, matching, and matroid problems. For NP-complete discrete optimization problems, current research literature includes the following...
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Clique cover (redirect from Clique partition problem)
clique cover is NP-hard, and its decision version is NP-complete. It was one of Richard Karp's original 21 problems shown NP-complete in his 1972 paper...
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Feedback vertex set (category NP-complete problems)
three. Karp's reduction also implies the NP-completeness of the feedback vertex set problem on undirected graphs, where the problem stays NP-complete on graphs...
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Richard Karp's subsequent paper, "Reducibility among combinatorial problems", generated renewed interest in Cook's paper by providing a list of 21 NP-complete...
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Maximum cut (redirect from Max-cut problem)
satisfiability problem). The weighted version of the decision problem was one of Karp's 21 NP-complete problems; Karp showed the NP-completeness by a reduction...
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Satisfiability (redirect from Satisfiability problem)
: 755 2-satisfiability Boolean satisfiability problem Circuit satisfiability Karp's 21 NP-complete problems Validity Constraint satisfaction Boolos, Burgess...
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