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Questions related to the (computational) complexity of solving problems

1 vote
3 answers
538 views

What time complexity relative to input size is that?

If an algorithm takes two numbers $b$ and $n$ and its input size satisfies $O(\log_2{n} + \log_2{b})$ plus its time complexity satisfies $O(b \log_{2}{n})$, what is the time complexity relative to the …
0 votes
3 answers
334 views

Size of instance after reduction

A decision problem $C$ is $NP$-complete if $C$ is in $NP$, and every problem in $NP$ is reducible to $C$ in polynomial time. Reduction means transforming an instance of one problem $A$ to an instance …
1 vote
1 answer
1k views

Time complexity - least upper bound

I know that Big $O$ notation is used to describe the upper bound of running time of an algorithm, if we consider time complexity of that algorithm. However, I'm not sure why the following is not state …