# Questions tagged [time-complexity]

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

267 questions
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### What's the complexity of Spearman's rank correlation coefficient computation? [closed]

I've been studyin' the Spearman's rank correlation coefficient. If computed for two list that have both size $N$, what's the complexity of the algorithm? $O(N)$ ? Thanks in advance.
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### The computational complexity of matrix multiplication

I am looking for information about the computational complexity of matrix multiplication of rectangular matrices. Wikipedia states that the complexity of multiplying $A \in \mathbb{R}^{m \times n}$ by ...
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### Algorithms with finite expected running time and infinite variance

I am working on an algorithm for which the running time is a random variable $X$ that has finite expected value, but infinite variance. Are there examples of other algorithms for which this is the ...
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### Are sorting algorithms approaching linear time? [closed]

I see some algorithms can do sorting in O(nloglogn) time. Is it reasonable to assume that as research progresses, more and more will be done to logarithm the extra time e.g. next research will produce ...
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### Worst-case asymptotic-complexity of the Set-cover problem?

What's the worst-case asymptotic-complexity of the Set-cover problem in Big O notation? I've been developing some novel techniques to try and solve this problem but am having trouble finding the ...
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### Optimality of Greedy algorithm for minimization Knapsack Problem

Given items with weight $w_i$ and profits $p_i$, minimization Knapsack problem is to pick a subset of items $I$, s.t. $\sum_{i\in{I}}{w_i} \geq W$ and $\sum_{i\in{I}}{p_i}$ is minimized. The greedy ...
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### Complexity of greedy coloring

I was looking at some heuristics for coloring and found this book on Google books: Graph Colorings By Marek Kubale They describe the Greedy algorithm as follows: ...
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### “Exact” (not just the order) computational complexity of eigenvalue decomposition

Does anyone know what the eigenvalue decomposition of a general n x n complex matrix is? By complexity I mean the number of multiplication operations. I know from another question posted on this site ...
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### Complexity of the directed Steiner tree problem on special graph classes

I am interested in the complexity of the directed Steiner tree problem: Given a weighted digraph $D=(V,E)$, a root $r\in V$ of $D$, and a set of terminals $T\subseteq V$. The objective is to find a ...
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### Lower bounds on batched query search

I am not much in the field of databases. But the problem I m facing is the following: given a database $D$, we receive a batch of distinct queries $Q = \{q_1, ..., q _k\}$, where each $q_i$ is a ...
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### How can a problem have complexity $O(n^{2+\epsilon})$ for all $\epsilon > 0$?

For instance, it is believed that for any $\epsilon>0$ there is an algorithm for matrix multiplication that runs in $O(n^{2+\epsilon})$, but possibly no algorithm that runs in $O(n^2)$. How is this ...
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### Indexing over all possible functions in better than linear time

Given two sets X and Y, the number of functions mapping X to Y is $\vert Y\vert^{\vert X \vert}$. In particular I am interested in binary strings of relatively small length, e.g. 8. There are $2^8$ (...
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### NP-Completeness of Certain Bounded Degree Graphs [closed]

I was studying time complexity when it comes to bounded degree graph problems and I was wondering if I can get help with the following two problems. 1) Is the set of all (G, k) where G is a graph ...
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### Optimal term frequency analysis

I'm looking for a term-frequency analysis structure which is more efficient than a hash table in terms of worst-case performance and speed in practice. I specifically care about the operations insert ...
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### What is the fastest algorithm to compute rank of a rectangular matrix?

Given an $m \times n$ matrix (assuming $m \ge n$), what is the fastest algorithm to compute its rank and basis of the columns? I am aware it can be solved through linear matroid intersection, which ...
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### Explaining input-size of integral arguments to undergraduate CS students

When I teach undergraduate algorithms, the students have no problem accepting that two n-bit numbers can be added in $O(n)$ time, or that modular exponentiation takes $O(n^3)$ time. But when we get ...
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### What happens if we improve the time hierarchy theorems?

In a nutshell, the time hierarchy theorems say that a Turing machine can solve more problems if it has more time for computation. In detail for deterministic TM and time-constructable functions $f,g$ ...
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### Can Merlin convince Arthur about a certain sum?

Merlin, who has unbounded computational resources, wants to convince Arthur that $$m|\sum_{p\le N,\ p\text{ prime}}p^k$$ for $(N,m,k)$ with $k=O(\log N)$ and $m=O(N).$ Computing this sum in the ...
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### What is the “right” definition of upper and lower bounds?

Let $f(n)$ be the worst case running time of a problem on input of size $n$. Let us make the problem a bit weird by fixing $f(n) = n^2$ for $n=2k$ but $f(n) = n$ for $n=2k+1$. So, what is the lower ...
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### Lower Bounds for Data Structures

Are results known which rule out the existence of "too-good-to-be-true" data structures? For example: can one add $Split$ and $Join$ functionality to an order maintenance data structure (see Dietz ...