# 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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### how is time complexity defined in computational learning theory

In general, when we say an algorithm $A$ PAC learns $C$ in time $t$, we say $A$ takes time $t$ before outputting a hypothesis $h$, and the hypothesis can be evaluated (on every $x$) in time $t$. Now ...
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### Time complexity of finding a point of infinite order on a rank 1 elliptic curve over Q

As an outsider, it sounds like a lot of progress has been made on understanding rank 1 elliptic curves over Q. Much of the BSD conjecture is known for rank 1, and Heegner points provide a way in ...
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### Example problem that is not in $2^{o(n)}$ but could be solved in $O(2^{cn})$ for any $c > 0$ (suggested by wording of ETH)

In the wikipedia article on Time Complexity it is written that: The exponential time hypothesis (ETH) is that 3SAT, the satisfiability problem of Boolean formulas in conjunctive normal form with, ...
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### Parallel building time of a k-d tree on n points with n processors

Given a point set with $n$ points to build a k-d tree on. We have $n$ processors available. What is the time-optimal building time for the k-d tree? A straight forward parallelization would be as ...
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### Minimize The Number of Connected Components in Hit-map of A Boolean Matrix

Suppose there is a matrix with the value of 0 and 1. The hit-map of the matrix (0 is blue and 1 is red) create some connected component (see the following figure as an instance): Is there any ...
1 vote
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### Worst case polynomial in elimination theory under rank conditions?

Given $n$ polynomials $h_1(x_1,\dots,x_{2n}),\dots,h_{2n}(x_1,\dots,x_{2n})\in\mathbb Z[x_1,\dots,x_{2n}]$ where each of $h_1(x_1,\dots,x_{2n}),\dots,h_{2n}(x_1,\dots,x_{2n})$ is homogeneous of degree ...
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I hope this is a suitable place to ask this question. An addition chain of size $n$ is a sequence $x_1, \dots, x_n$, where $x_1$ is fixed to 1 and $x_i = x_j + x_k$ for some $j,k < i$. I am ...
1 vote
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### EXPSPACE proof and its implications

I'm dealing with the min-max regret 0-1 Integer Linear Programming problem (MMR-ILP, for short), which is formulated as below. \begin{equation} \label{eq:nip_obj} \min_{x \in \Phi} \sum_{i = 1}^n ...
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### Time complexity of exponentiating s-sparse matrices

Could someone suggest me a reference which discusses the time complexity of algorithms meant for exponentiating (finding $e^A$ approximately given $A$) s-sparse matrices, along with their error rates? ...