# 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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### One Stack, Two Queues

background Several years ago, when I was an undergraduate, we were given a homework on amortized analysis. I was unable to solve one of the problems. I had asked it in comp.theory, but no ...
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### Complexity of Finding the Eigendecomposition of a Matrix

My question is simple: What is the worst-case running time of the best known algorithm for computing an eigendecomposition of an $n \times n$ matrix? Does eigendecomposition reduce to matrix ...
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### Using lambda calculus to derive time complexity?

Are there any benefits to calculating the time complexity of an algorithm using lambda calculus? Or is there another system designed for this purpose? Any references would be appreciated.
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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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### What are some algorithms where space complexity tends to be the limiting factor in practice?

Time complexity can't be any lower than space complexity (at least one operation is required to use a unit of memory), so what are some algorithms where space actually tends to be the limiting factor? ...
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### To what extent can an algorithm predict the time complexity an arbitrary input program?

The Halting problem states that it is impossible to write a program that can determine if another program halts, for all possible input programs. I can, however, certainly write a program that can ...
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### Adding integers represented by their factorization is as hard as factoring? Reference request

I'm looking for a reference for the following result: Adding two integers in the factored representation is as hard as factoring two integers in the usual binary representation. (I'm pretty sure ...
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### Can you decide equivalence for monotone Boolean expressions that do not contain negation in PTIME?

Is the following problem in PTIME, or coNP-hard: Given two Boolean expressions $e_1$ and $e_2$ in variables $x_1,\dots,x_n$, without negation (ie, the expressions are entirely built up via $\wedge$ ...
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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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### What is the background in algebraic geometry and representation theory needed for geometric complexity theory? [duplicate]

I'm a mathematics student in my junior year and I'm interested in computational complexity and specially geometric complexity theory. I'm going to learn algebraic geometry and representation theory ...
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### Counting the number of vertex covers: when is it hard?

Consider the #P-complete problem of counting the number of vertex covers of a given graph $G = (V, E)$. I'd like to know if there is any result showing how the hardness of such problem varies with ...
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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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### Linear time in-place riffle shuffle algorithm

Is there a linear time in-place riffle shuffle algorithm? This is the algorithm that some especially dextrous hands are capable of performing: evenly dividing an even-sized input array, and then ...
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### Does $∩_{ε>0} \mathrm{DTIME}(O(n^{2+ε})) = \mathrm{DTIME}(n^{2+o(1)})$?

I expect the answer is no, but I could not actually construct a counterexample. The difference is that in $∩_{ε>0} \mathrm{DTIME}(O(n^{2+ε}))$, we might not be able to pick an $O(n^{2+ε})$ ...
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### An algebra of complexity classes

A key feature of unrelativized computation is its composability out of smaller fragments, and to partially capture the composability, I came up with an algebra of fine-grained complexity classes. For ...
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### Is Quasi-polynomial time in PSPACE?

I had done some search on this but I was not able to find an answer either way. Huck answered it fully. Thanks :)
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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 ...
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### What is a natural problem in theory of computation?

In Stephen Cook's paper on the P vs NP problem,[1] he states the following [2]: Feasibility Thesis: A natural problem has a feasible algorithm iff it has a polynomial-time algorithm. My question ...
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### Gaussian Elimination in terms of Group Action

Gaussian elimination makes determinant of a matrix polynomial-time computable. The reduction of complexity in computing the determinant, which is otherwise sum of exponential terms, is due to ...
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### 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 ...
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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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### Are there languages decidable in linear time by RAM machines that have superlinear time complexity lower bounds for Multitape Turing machines?

Question: Are there languages decidable in linear time by RAM machines that have superlinear time complexity lower bounds for Multitape Turing machines? Background: I recently stumbled upon the ...
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### Equivalent definitions of time constructibility

We say that a function $f:\mathbb{N}\rightarrow\mathbb{N}$ is time-constructible, if there exists a deterministic multi-tape Turing machine $M$ that on all inputs of length $n$ makes at most $f(n)$ ...
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