Examples of using Np-complete problems in English and their translations into Romanian
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NP-complete problems.
The Boolean satisfiability problem is one of many such NP-complete problems.
Solving NP-complete problems.
That is, any NP problem can be transformed into any of the NP-complete problems.
Solving NP-complete problems and the comparison of different solving techniques(14).
The clique decision problem is NP-complete(one of Karp's 21 NP-complete problems).
NP-complete problems are often addressed by using heuristic methods and approximation algorithms.
Elements of computational geometry* Solving NP-complete problems and comparison of different solutions Backtracking.
Some NP-complete problems, indicating the reductions typically used to prove their NP-completeness.
The consequences, both positive and negative,arise since various NP-complete problems are fundamental in many fields.
As for most NP-complete problems, it may be enough to find workable solutions even if they are not optimal.
The directed and undirected Hamiltonian cycle problems were two of Karp's 21 NP-complete problems.
Because of this,it is often said that NP-complete problems are harder or more difficult than NP problems in general.
Viewing a decision problem as a formal language in some fixed encoding,the set NPC of all NP-complete problems is not closed under.
Further, some NP-complete problems actually have algorithms running in superpolynomial, but subexponential time such as O(2√nn).
But such changes may pale in significance compared to the revolution an efficient method for solving NP-complete problems would cause in mathematics itself.
It is NP-complete, one of Karp's 21 NP-complete problems.[6] It is also fixed-parameter intractable, and hard to approximate.
In the field of cryptography, the term knapsack problem is often used to refer specifically to the subset sum problem andis commonly known as one of Karp's 21 NP-complete problems.[30].
In computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete. .
NP-complete problems are studied because the ability to quickly verify solutions to a problem(NP) seems to correlate with the ability to quickly solve that problem(P).
At 1971 STOC conference,there was a fierce debate among the computer scientists about whether NP-complete problems could be solved in polynomial time on a deterministic Turing machine.
NP-complete problems are the most difficult known problems." Since NP-complete problems are in NP, their running time is at most exponential.
Nobody has yet been able to determine conclusively whether NP-complete problems are in fact solvable in polynomial time, making this one of the great unsolved problems of mathematics.
A key reason for this belief is that after decades of studying these problems no one has been able to find a polynomial-time algorithm for any of more than 3000 important known NP-complete problems(see List of NP-complete problems).
At present, all known algorithms for NP-complete problems require time that is superpolynomial in the input size, and it is unknown whether there are any faster algorithms.
Note that this diagram ismisleading as a description of the mathematical relationship between these problems, as there exists a polynomial-time reduction between any two NP-complete problems; but it indicates where demonstrating this polynomial-time reduction has been easiest.
However, there are algorithms for NP-complete problems with the property that if P= NP, then the algorithm runs in polynomial time(although with enormous constants, making the algorithm impractical).
On the other hand, there are NP-problems with at most one solution that are NP-hard under randomized polynomial-time reduction(see Valiant- Vazirani theorem)."Solving NP-complete problems requires exponential time." First, this would imply P≠ NP, which is still an unsolved question.
While a method for computing the solutions to NP-complete problems using a reasonable amount of time remains undiscovered, computer scientists andprogrammers still frequently encounter NP-complete problems.
In 1972, Richard Karp proved that several other problems were also NP-complete(see Karp's 21 NP-complete problems); thus there is a class of NP-complete problems(besides the Boolean satisfiability problem).