Questions tagged [k-wise-independence]

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Family of functions with properties similar to k-wise independent hash functions

I am looking for a family of functions that has similar properties to a family of $\ell$-wise independent hash functions. The goal is to hash $\ell$ pairwise different bit strings of length $k$ to a ...
Dave's user avatar
  • 183
1 vote
1 answer

Efficient randomness reduction using k-wise independence

Consider a randomized algorithm with runtime $n$, which succeeds with high probability. The algorithm uses $O(n)$ uniformly random bits. Now it is given that we can replace these uniformly random ...
smapers's user avatar
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7 votes
2 answers

Analogue of $k$-wise independence for other distributions than uniform

I am looking for the name of the following notion (in order to look it up for myself), and possibly pointers to the corresponding literature. Let $D$ be a fixed distribution over $\{0,1\}^n$, and $1\...
Clement C.'s user avatar
  • 4,451
3 votes
1 answer

Optimal bounds for $k$-wise non-uniform random bits

Let $k\geq 2$ be a constant (in my case, $k=4$), and $n,t \geq 0$ be integers such that $2^t \leq n$. What is the smallest sample space (or, equivalent, how many true independent random bits are ...
Clement C.'s user avatar
  • 4,451
9 votes
0 answers

Fourth(?) moment method for minimum value

I would like to lower bound the quantity $\Pr[X\ge t, Y\ge t]=\Pr[\min(X,Y)\ge t]$ using the small moments of $X$, $Y$ and $XY$. In particular I am interested in the case where $E[X]=E[Y]=0$, but $E[X ...
Thomas Ahle's user avatar
3 votes
1 answer

Notion similar to k-wise independence

I want to construct a family of functions $H:\{0,1\}^n \rightarrow \{0,1\}$ with a property that is similar to k-wise independence. Specifically, I want $H$ to satisfy the following property. Let $k$ ...
NotSo Smart's user avatar
4 votes
1 answer

How well do subspaces hit sets

Let $S\subset F_2^n$ be a subset of size $\epsilon\cdot 2^n$. Say I choose a random subspace $V$ of dimension $k$ in $F_2^n$. I want to know what is the smallest $k$ such that $V$ `hits' $S$, i.e., $V\...
relG's user avatar
  • 209
8 votes
1 answer

A bounded-independence variant of the Berry-Esseen theorem

I came across a presentation by Ryan O'Donnell regarding invariance principles. After proving the Berry-Esseen theorem, there is a slide that discusses extensions of the theorem and one that is ...
Dean's user avatar
  • 225
10 votes
1 answer

Can we construct a k-wise independent permutation on [n] using only constant time and space?

Let $k>0$ be a fixed constant. Given an integer $n$, we want to construct a permutation $\sigma \in S_n$ such that: The construction uses constant time and space (i.e. preprocessing takes constant ...
Sariel Har-Peled's user avatar