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Results tagged with time-complexity
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user 83257
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.
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Knapsack dynamic programming complexity issue for $W=1$, is it $O(n)$?
The 0-1 knapsack problem is given by
$$\begin{align}&\text{maximize } \sum_{i=1}^n v_ix_i,\tag{P1}\\&
\text{subject to } \sum_{i=1}^n w_i x_i \leq W,\\&\text{and } x_i \in \{0,1\}.\end{align}$$
Runn …
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Examples of higher order algorithms ($\mathcal{O}(n^4)$ or larger)
The problem of $1$-processor gap scheduling of $n$ jobs has time complexity $O(n^7)$.
The paper is available here.
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Find median of unsorted array in $O(n)$ time
There is a randomized Monte Carlo algorithm to do this. It is described in [MU2017]. It is a linear time algorithm that fails to produce a solution with probability at most $n^{-1/4}$. As discussed in …
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