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Maximum volume submatrix – Problem of selecting the best conditioned subset of a larger matrix. This class of problem is associated with Rank revealing QR factorizations and D optimal experimental design. [39] Minimal addition chains for sequences. [40]
Counting problems are a subset of a broader class of problems called function problems. A function problem is a type of problem in which the values of a function f : A → B {\displaystyle f:A\to B} are computed.
In this theory, the class P consists of all decision problems (defined below) solvable on a deterministic sequential machine in a duration polynomial in the size of the input; the class NP consists of all decision problems whose positive solutions are verifiable in polynomial time given the right information, or equivalently, whose solution can ...
NP is a class of decision problems; the analogous class of function problems is FNP. The only known strict inclusions come from the time hierarchy theorem and the space hierarchy theorem , and respectively they are N P ⊊ N E X P T I M E {\displaystyle {\mathsf {NP\subsetneq NEXPTIME}}} and N P ⊊ E X P S P A C E {\displaystyle {\mathsf {NP ...
The complexity class NP, on the other hand, contains many problems that people would like to solve efficiently, but for which no efficient algorithm is known, such as the Boolean satisfiability problem, the Hamiltonian path problem and the vertex cover problem. Since deterministic Turing machines are special non-deterministic Turing machines ...
Similarly, a problem hard for a class C is called C-hard, e.g. NP-hard. Normally, it is assumed that the reduction in question does not have higher computational complexity than the class itself. Therefore, it may be said that if a C-complete problem has a "computationally easy" solution, then all problems in "C" have an "easy" solution.
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Class of computational decision problems for which any given yes-solution can be verified as a solution in polynomial time by a deterministic Turing machine (or solvable by a non-deterministic Turing machine in polynomial time). NP-hard Class of problems which are at least as hard as the hardest problems in NP.