Information om | Engelska ordet NP-COMPLETE

Exempel på hur man kan använda NP-COMPLETE i en mening

• The Hamiltonian path problem and the Hamiltonian cycle problem belong to the class of NP-complete problems, as shown in Michael Garey and David S.
• For instance, a problem is NP-complete if it belongs to NP and all problems in NP have polynomial-time many-one reductions to it.
• Computationally, the problem is NP-hard, and the corresponding decision problem, deciding if items can fit into a specified number of bins, is NP-complete.
• In 1971 he co-developed with Jack Edmonds the Edmonds–Karp algorithm for solving the maximum flow problem on networks, and in 1972 he published a landmark paper in complexity theory, "Reducibility Among Combinatorial Problems", in which he proved 21 problems to be NP-complete.
• Although the conjecture itself remains open, it has led toa large body of research on the structure of NP-complete sets, culminatingin Mahaney's theorem on the nonexistence of sparse NP-complete sets.
• In 1971, Stephen Cook and, working independently, Leonid Levin, proved that there exist practically relevant problems that are NP-complete – a landmark result in computational complexity theory.
• Determining whether for graphs G and H, H is homeomorphic to a subgraph of G, is an NP-complete problem.
• Since the P versus NP problem is unresolved, it is unknown whether NP-complete problems require superpolynomial time.
• Graph coloring has been studied as an 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, and at approximately the same time various exponential-time algorithms were developed based on backtracking and on the deletion-contraction recurrence of.
• 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.
• Cliques have also been studied in computer science: the task of finding whether there is a clique of a given size in a graph (the clique problem) is NP-complete, but despite this hardness result, many algorithms for finding cliques have been studied.
• The significance of NP-completeness was made clear by the publication in 1972 of Richard Karp's landmark paper, "Reducibility among combinatorial problems", in which he showed that 21 diverse combinatorial and graph theoretical problems, each infamous for its intractability, are NP-complete.
• Determining the achromatic number is NP-hard; determining if it is greater than a given number is NP-complete, as shown by Yannakakis and Gavril in 1978 by transformation from the minimum maximal matching problem.
• Although it is possible to transform any two triangulations of the same polygon into each other by flips that replace one diagonal at a time, determining whether one can do so using only a limited number of flips is NP-complete.
• Although including the optimization constraints into the synaptic weights in the best possible way is a challenging task, many difficult optimization problems with constraints in different disciplines have been converted to the Hopfield energy function: Associative memory systems, Analog-to-Digital conversion, job-shop scheduling problem, quadratic assignment and other related NP-complete problems, channel allocation problem in wireless networks, mobile ad-hoc network routing problem, image restoration, system identification, combinatorial optimization, etc, just to name a few.
• showed that the decision version of the betweenness problem (in which an algorithm must decide whether or not there exists a valid solution) is NP-complete in two ways, by a reduction from 3-satisfiability and also by a different reduction from hypergraph 2-coloring.
• Graph partition into subgraphs of specific types (triangles, isomorphic subgraphs, Hamiltonian subgraphs, forests, perfect matchings) are known NP-complete.
• An algorithm for listing all maximal independent sets or maximal cliques in a graph can be used as a subroutine for solving many NP-complete graph problems.
• Like many other combinatory and logic puzzles, Masyu can be very difficult to solve; solving Masyu on arbitrarily large grids is an NP-complete problem.
• The MAX-SAT problem is OptP-complete, and thus NP-hard, since its solution easily leads to the solution of the boolean satisfiability problem, which is NP-complete.

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