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The amount of time resources (number of atomic operations or machine steps) required to solve a problem expressed in terms of input size. If your question concerns algorithm analysis, use the [runtime-analysis] tag instead. If your question concerns whether or not a computation will *ever* finish, use the [computability] tag instead. Time-complexity is perhaps the most important sub-topic of complexity theory.

2 votes
1 answer
4k views

Does NP mean verifiable in polynomial time or solvable in polynomial time? [duplicate]

Is NP defined as verifiable in polynomial time, or solvable in polynomial time? Verifiable meaning that the solution can be checked in polynomial time, and solvable meaning that the solution can be fo …
Alecto's user avatar
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1 vote
0 answers
186 views

Highest useful complexity class

Aside from problems such as the halting problem, which aren't computable, are there any useful problems in computer science that can only be solved in time $O(2^{2^n})$, or in time $O((n!)!)$? I've he …
Alecto's user avatar
  • 564
8 votes
2 answers
1k views

Could a quantum computer perform linear algebra faster than a classical computer?

Supposing we had a quantum computer with a sufficient number of qubits, could we use it to do linear algebra faster than we could with a classical computer? What sort of speedup could we expect? Has a …
Alecto's user avatar
  • 564
2 votes
1 answer
177 views

Best combination of values pulled from a matrix

What is the fastest way to select $n$ values from an $n$ by $n$ matrix such that each value comes from a different row and column and the sum of those n values is minimized? For example, given the ma …
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