# Questions tagged [time-complexity]

Time complexity of decision problems or relations among time-bounded complexity classes. (Use the [analysis-of-algorithms] tag for the time taken by particular algorithms.)

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### Example of context-free grammar that triggers exponential behaviour without memoization in RD parsers

It is often said that memoization brings the complexity of recursive-descent parsers from exponential to polynomial. However, I had a hard time finding an example grammar that triggers the exponential ...
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### Why does the construction step of Aho-Corasick take linear time in the number of nodes?

The original paper's analysis of this, as far as I can tell is this: "THEOREM 3. Algorithm 2 requires time linearly proportional to the sum of the lengths of the keywords. PROOF. Straightforward." ...
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For $\vec{d} \in \mathbb{N}^n$, let $Q(\vec{d}) \subset \mathbb{N}^n$ be the set of vertices of the $n$-dimensional cube scaled in the direction of the $i$-th coordinate by $d_i$, i.e. $Q(\vec{d} = \{... 2 votes 2 answers 214 views ### Number of SAT checks that are needed to find all combinations of subset of boolean variables of a propositional formula Please mind that I sometimes lack formal mathematical knowledge and English is not my first language, so I might miss the right words. Please change the tile if needed. Also, I have choosen this site ... 14 votes 1 answer 1k views ### Distinguishing between two coins It is well known that the complexity of distinguishing an$\epsilon$biased coin from a fair one is$\theta(\epsilon^{-2})$. Are there results for distinguishing a$p$coin from a$p+\epsilon$coin? I ... 1 vote 2 answers 287 views ### Lower-bound of a decision problem [closed] What's the lower-bound of the decision problem that decides: Whether there is at least one element A[i] such that A[i] = i in a sorted array A of non-negtive integers? (An example is A = {0,1,1,3,4,4,... 0 votes 0 answers 3k views ### Most efficient algorithm to search an unsorted array with a very precise data structure (I apologize in advance if this question sounds a bit practical, but I suspect it might have an interesting theoretical aspect.) I have a (large) array of data, not completely sorted, but with which ... 12 votes 1 answer 518 views ### Does Kannan's theorem imply that NEXPTIME^NP ⊄ P/poly? I was reading a paper of Buhrman and Homer “Superpolynomial Circuits, Almost Sparse Oracles and the Exponential Hierarchy”. On the bottom of page 2 they remark that the results of Kannan imply that$... 204 views

### Consequences of nondeterminism speeding up deterministic computation

If $\mathsf{NP}$ contains a class of superpolynomial time problems, i.e. for some function $t \in n^{\omega(1)}$, $\mathsf{DTIME}(t) \subseteq \mathsf{NP}$, then if follows from the deterministic ...
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1 vote
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### Calculation of Recursive Spawning

I'm reading the book Introduction to Algorithms (Cormel et al., 2009) on the chapter about multithreaded algorithms, and I'm confused about the following: We must also account for the overhead of ...
1 vote
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Suppose an algorithm that receive an input array of $n$ elements and it performs a task over each element. All tasks are independent and take $O(k)$ each (being $k$ a variable). Since all tasks are ...
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### Can we compute $n$ from the bits of $3^n$ in $O(n)$ time?

I'm seeking an efficient algorithm for the problem: Input: The positive integer $3^n$ (stored as bits) for some integer $n \geq 0$. Output: The number $n$. Question: Can we compute $n$ from the bits ...
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### Time complexity analysis of random forest and k-means?

I am working with random forest for a supervised classification problem, and I am using the k-means clustering algorithm to split the data at each node, where $n$ is the number of points, $K$ is ...
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### Is there any task where classical computers outperform quantum computers?

Everybody knows that there are whole classes of problems which quantum computers are able to solve much faster (i.e. with fewer instructions) than classical computers. Is there any problem for which ... 4k views

### Compute Time Complexity of Neural network, SVM and other classification algorithms

I would like to know what is the asymptotic time complexity analysis for general models of Back-propagation Neural Network, SVM and Maximum Entropy. Does it just depend on number of features included ...
1 vote
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### Time complexity of clustering based on random walk

What is the time complexity of the following algorithm (from this paper suggested by Zhou) to partition directed graph? Can I use the complexity of eigen vector computation for this purpose? The ...
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### Constant time search for rod segment

(I tried to ask at SO but maybe this has more to do with the CS theory.) Suppose I have a rod which I cut to pieces. Given a point on the original rod, is there a way to find out which piece it ...
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### Flood fill vs depth first search

Is the flood fill algorithm the same as depth first search? If not, how do they differ in complexity?
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### Advanced techniques for determining complexity lower bounds

Some of you may have been following this question, which was closed due to not being research level. So, I'm extracting the part of the question which is at a research level. Beyond the "simpler" ...
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### How are lower bounds for computational complexity proved? [closed]

As the title says, how are lower bounds for computational complexity proved? I'm interested why it is possible to say that a certain algorithm cannot run in faster time than some lower bound. ...
I'm trying to understand the full bit-complexity of computing the determinant of an $n\times n$ integer matrix, with each entry represented by $M$ bits. I would like to know what is the state-of-the-...