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Questions tagged [probabilistic-algorithms]

Questions about (typically randomized) algorithms that can produce no or an incorrect answer with a certain probability.

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Possible to construct a probabilistic halting problem solver?

I'm a CS undergrad so my math/CS knowledge is not that deep so please correct me if my premise is flawed or I have made some incorrect assumptions. So I was thinking, much in the way that some ...
• 211
403 views

Find expectation with Chernoff bound

We have a group of employees and their company will assign a prize to as many employees as possible by finding the ones probably better than the rest. The company assigned the same $2$ tasks to every ...
• 31
541 views

Choosing error rates for probabilistic algorithms

Probabilistic algorithms often have a parameter that allows one to tune the error rate, typically by running the algorithm repeatedly. This often gives an error rate of something like $2^{-k}$ for $k$ ...
754 views

Derandomization of vertex cover algorithm

I have the following randomized-algorithm for the vertex cover problem. Let $B_0$ be the output set: Fix some order $e_1, e_2,...,e_m$ over all edges in the edge set E of G, and set $B_0=∅$. Add to ...
3k views

How to get expected running time of hash table?

If I have a hash table of 1000 slots, and I have an array of n numbers. I want to check if there are any repeats in the array of n numbers. The best way to do this that I can think of is storing it in ...
• 553
8k views

Deleting in Bloom Filters

I know that standard Bloom Filters only have operations like inserting elements and checking if an element belongs to filter, but are also some modification of Bloom filters which enable a delete ...
• 259
904 views

Prove or refute: BPP(0.90,0.95) = BPP

I'd really like your help with the proving or refuting the following claim: $BPP(0.90,0.95)=BPP$. In computational complexity theory, BPP, which stands for bounded-error probabilistic polynomial time ...
• 472
7k views

What do we know about $NP \cap co-NP$?

What do we need about the intersection of $NP$ and $co-NP$ apart from the fact that $P$ is a subset of it? (beyond what these answers here say, What do we know about NP ∩ co-NP and its relation to ...
• 1,145
613 views

Given a RxC grid, how to generate N 2D points randomly such that no 3 points are collinear?

Context, I have a geometric algorithm that is sensitive to collinear points and receives as input a list of points in 2D generated randomly. Suppose that I have a Boolean function nonCollinear(x,y,z) ...
• 265
769 views

What is an example of a weakly universal hash function that is not pairwise independent?

A family of hash functions $H_w$ is said to be weakly universal if for all $x \ne y$ : $$P_{h \in H_w}(h(x) = h(y)) \leq 1/m$$ Here the function $h:U \rightarrow [m]$ is chosen uniformly from the ...
• 996
532 views

Why do Bloom filters work?

Let's say I am using Bloom filters to create a function to check if a word exists in a document or not. If I pick a hash function to fill out a bit bucket for all words in my document. Then if for a ...
• 143
3k views

Average Case Analysis for finding max and min value on an array

Given the following algorithm, to find the maximum and minimum values of an array - don't mind the language: ...
• 155
3k views

What would be a decent threshold for classification problem?

I'm using machine-learning algorithms to solve binary classification problem (i.e. classification can be 'good' or 'bad'). I'm using SVM based algorithms, ...
• 133
498 views

Can BPP be bounded around any constant other than 1/2?

A language $L$ is in BPP if there exists a randomised TM such that it outputs a correct answer with probability at least $1/2+1/p(n)$ for some polynomial $p(n)$, where $n$ is the length of the input. ...
• 1,319
178 views

Are there any practical differences between a Turing machine with a PRNG and a probabilistic Turing machine?

Say I plugged in a hardware true-random number generator (TRNG) to my computer, then wrote programs with output that depends on the TRNG's output. Can it do anything non-trivial that a Turing machine ...
• 151
1 vote
244 views

Uniform sampling with constraints

Suppose one wants to uniformly sample a string $w$ of a given length over a finite alphabet, such $w$ satisfies a set of structural constraints (such as - "the third character has to be equal to the ...
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