# 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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### Introduction to complexity calculation

I want to understand how is the probability of each input is distributed / defined, because it looks so abstract for me, for example here is a question write an algorithm to calculate the median of 3 ...
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### computational complexity of sparse matrix powers

Given a sparse matrix $A$ with $nnz(A)$ denoting the number of non-zero entries in it. What is the computational complexity of computing $A^k$, for some positive integer $k$? As $k$ gets larger, I ...
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### Statements equivalent to strongly polynomial time linear programming

Say a problem is SPT iff it admits an SPT algorithm. What statements of interest are known to be equivalent to "LP is SPT"? Examples: "linear feasibility solving is SPT" (due to ...
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### Complexity of reachability in fractal mazes with traps

Is reachability in fractal mazes with traps EXPTIME complete? A fractal maze includes one or more copies of itself. For example, see the question Decidability of Fractal Maze or Puzzling ...
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### Strongly polynomial time algorithm for shortest convex combination

Problem: Let $S$ be a finite set of vectors. Let $C$ be their convex hull. Compute $\operatorname{argmin}_{x \in C} \|x\|$. Reference 1 gives an algorithm for this problem that is finite-time (Section ...
1 vote
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### Computational complexity and general relativity

According to general relativity, the time that a Turing Machine near a massive object spends on computing every step is longer than the time that the Turing Machine far awayfrom a massive object ...
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### What Complexity Class is this? Is this already known?

Let's call this the Path Game. For this example, lets imagine a 16x16 grid: Some of the squares in this grid are "deadly." If you step on it, you must restart and try to go over again. We ...
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### list of 3-CNF formula that can be solved in polynomial time

Suppose i want to program a 3-SAT solver. I want my solver to first check whether a formula is in the list of 3-CNF that currently known can be solved in polynomial time before resorting to brute ...
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1 vote
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### 3-SAT runtime if an optimal order to eliminate possible solutions is known

As a mental exercise I have been playing around with the 3-SAT problem, but I am having difficulty proving or disproving the usefulness of a current idea that I am playing around with. My current ...
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### Subset Sum Problem exact Algorithm (hypothetical)

Let assume there is way to apply a divide & conquer approach to the classical subset sum solver of Horowitz and Sahni. And for this, we design a decomposition function, when applied to the ...
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### Lower bound for the OR problem

Let us have booleans $x_1, \cdots, x_n$. Any algorithm that determines $\bigvee_1^n x_i$ with probability at least $2/3$ requires $\Omega(n)$ time. It is not too difficult to prove this, but the proof ...
### Finding the best $k-$subset which maximizes a matrix sum
Let $M\in \mathbb{R}^{N\times N}$ be a given matrix and $k\ge 2$ be a given integer. Then my question is the following optimization problem: Is there a polynomial-time solution to the following ...
This paper on universal search mentions (on pp. 6-7) that proof checking can be done in $O(n^2)$ where $n$ is the length of the proof. Is this optimal? I don't want to specify the problem too ...