NP-hard problem

[/ɛn-piː-hɑːrd ˈprɒbləm/]
nounpl: NP-hard problems
problema NP-difícil
1. A computational problem in complexity theory that is at least as difficult as the hardest problems in NP (nondeterministic polynomial time), meaning no known polynomial-time algorithm exists to solve it and it is unlikely one will ever be found.
The traveling salesman problem is a classic example of an NP-hard problem.
O problema do caixeiro viajante é um exemplo clássico de um problema NP-difícil.
2. A problem for which finding a solution is computationally intractable, even though verifying a proposed solution may be feasible.
Scheduling optimization is an NP-hard problem commonly encountered in logistics.
A otimização de agendamento é um problema NP-difícil comumente encontrado em logística.
This is specialized terminology primarily used in computer science, mathematics, and software engineering fields. It originated in American academic computer science in the 1970s with Stephen Cook and Richard Karp's foundational work. In Brazil and Portugal, the term is used identically in technical contexts, though it remains primarily confined to academic and professional computing communities rather than general discourse.
Synonyms / Sinônimos
computationally intractable problemNP-complete problem (related but distinct)hard computational problem
Antonyms / Antônimos
polynomial-time solvable problemP problemtractable problem

Regional Variations

General Brazilian Portuguese
problema NP-difícil
Standard term used in computer science education and research
General Brazilian Portuguese
problema NP-completo
Related term; sometimes used interchangeably but technically distinct
Portugal
problema NP-difícil
Same standard usage as in Brazil
USA/English-speaking
NP-hard problem
Original term; widely used in academic and professional settings

Related Words

NP-completecomputational complexityalgorithmpolynomial timeP vs NP problemapproximation algorithmheuristic solution

Related Idioms & Phrases

a computational nightmare
an intractable computational challenge
a problem without a polynomial solution
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