Information om | Engelska ordet NP-HARD

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

• In the theory of computational complexity, 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 exactly once and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research.
• As it is suspected, but unproven, that P≠NP, it is unlikely that any polynomial-time algorithms for NP-hard problems exist.
• In computational complexity theory, the complexity class NP-equivalent is the set of function problems that are both NP-easy and NP-hard.
• 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 2011, Laurent Bulteau, Guillaume Fertin, and Irena Rusu proved that the problem of finding the shortest sequence of flips for a given stack of pancakes is NP-hard, thereby answering a question that had been open for over three decades.
• For instance, for sparse graphs (graphs in which the number of edges is at most a constant times the number of vertices in any subgraph), the maximum clique has bounded size and may be found exactly in linear time; however, for the same classes of graphs, or even for the more restricted class of bounded degree graphs, finding the maximum independent set is MAXSNP-complete, implying that, for some constant c (depending on the degree) it is NP-hard to find an approximate solution that comes within a factor of c of the optimum.
• Solving multivariate quadratic equations (MQ) over a finite set of numbers is an NP-hard problem (in the general case) with several applications in cryptography.
• In computer science (particularly algorithmics), a polynomial-time approximation scheme (PTAS) is a type of approximation algorithm for optimization problems (most often, NP-hard optimization problems).
• 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.
• It is worth noting that inference problems like marginalization and maximization are NP-hard to solve exactly and approximately (at least for relative error) in a graphical model.
• In terms of computational complexity, the problem is an NP-hard problem reducible to the knapsack problem.
• The geometric version of the problem is also NP-hard, but not known to belong to NP, because of the difficulty of comparing sums of square roots; instead it lies in the class of problems reducible to the existential theory of the reals.
• Empirical risk minimization for a classification problem with a 0-1 loss function is known to be an NP-hard problem even for a relatively simple class of functions such as linear classifiers.
• In unconstrained (cartesian coordinate) space, this is an NP-hard problem requiring heuristic solutions such as Lloyd's algorithm, but in a network space it can be solved deterministically.
• The approximability of set covering is also well understood: a logarithmic approximation factor can be found by using a simple greedy algorithm, and finding a sublogarithmic approximation factor is NP-hard.
• Karp's reduction also implies the NP-completeness of the FVS problem on undirected graphs, where the problem stays NP-hard on graphs of maximum degree four.
• Finding minimum feedback arc sets and maximum acyclic subgraphs is NP-hard; it can be solved exactly in exponential time, or in fixed-parameter tractable time.
• 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.
• Because of this difficulty, it is NP-hard to find the smallest subgraph of a given graph G with the same reachability (its minimum equivalent graph).
• Semidefinite programs are important tools for developing approximation algorithms for NP-hard maximization problems.

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