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

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2
votes
1answer
51 views

Expected maximum bin load, for balls in bins with equal number of balls and bins [on hold]

Suppose we have $n$ balls and $n$ bins. We put the balls into the bins randomly. If we count the maximum number of balls in any bin, the expected value of this is $\Theta(\ln n/\ln\ln n)$. How can we ...
2
votes
1answer
36 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 ...
7
votes
0answers
79 views

Proof of PCP theorem

I am reading the proof of PCP theorem in Proof Verication and Hardness of Approximation Problems. The following paragraph appears in section 3 (page 4), "Outline of the Proof of the Main Theorem". ...
1
vote
0answers
40 views

PageRank and EigenTrust: How small should epsilon be?

For probabilistic algorithms such as PageRank and EigenTrust, the stopping case is given as $|R_{t+1} - R_{t}| < \epsilon$ (i.e. convergence is assumed). Neither the papers on EigenTrust or ...
1
vote
1answer
50 views

How are Bayesian Nets, Hidden Markov Chains, Conditional Random Fields and Neural Nets related?

I am having an AI exam in two weeks, and I am still figuring out certain concepts and ideas, related to Bayesian Nets, Hidden Markov Chains, Conditional Random Fields and Neural Nets (yes it is all ...
5
votes
1answer
69 views

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 ...
4
votes
1answer
82 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 ...
0
votes
1answer
69 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, ...
2
votes
1answer
30 views

finding a an object with constant velocity on an infinite grid in discrete time steps

Assume you have an object moving at a constant velocity(up, down, left, right) in a grid. You have unlimited resources (memory, time). At any given time step in the grid, you can "guess" the location ...
2
votes
2answers
216 views

why not just use a random number generator as a hash function?

I guess at the heart of this is that I don't really understand hash functions. One article says any function mapping objects to an object of fixed size: A hash function usually means a function ...
6
votes
3answers
179 views

Computer science problems related to music?

Are there any CS problems, preferably open, that are related to music or musical theory somehow? I would think of problem with musical notation but also probabilities when randomizing according to a ...
5
votes
3answers
238 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 ...
3
votes
1answer
168 views

Bloom filter and perfect hashing

Bloom filter use a hash function to test membership for S by checking if an item is present of not at the specified position. To mitigate the effect of hash collision, multiple functions are used, ...
4
votes
0answers
48 views

Signal-based Search

This is more of an open-ended information question, but to make it concrete, here's an example problem I have thought up: Consider an $N\times N$ grid, $N$ odd, and consider that a single chunk of ...
1
vote
1answer
64 views

How to sample uniformly from a stream of elements, some of which are unsuited?

I get values $x_t$ in an online fashion and want to buy "good" ones, where "good" means that some measure $P(x_t) >T$. Consider the following simple algorithm. ...
1
vote
1answer
311 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 ...
6
votes
2answers
143 views

Are probabilistic search data structures useful?

A SkipList provides the same $O(\log n)$ bounds for search as a balanced tree with the advantage that rebalancing isn't necessary. Since the SkipList is constructed using random coin flips, these ...
2
votes
0answers
43 views

Approximate target subset by intersecting other subsets

Let $S$ be a finite set of integers (this set contains about 200000 elements). Let $T \subset S$ be a particular subset of $S$ called target. $S$ keeps growing. So does $T$. Each new element of $S$ ...
1
vote
1answer
51 views

BPP clarification

I know that $\sf BPP[2/3,1/3]= BPP[\alpha,\beta]$ when $\alpha\lt\beta$, but I read something on Wikipedia which got me confused: In practice, an error probability of $1/3$ might not be ...
8
votes
1answer
296 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 ...
6
votes
1answer
121 views

BPP search: what does boosting correctness entail?

It is not really clear to me, how and if I can do boosting for correctness (or error reduction) on a BPP (bounded-error probabilistic polynomial-time) search problem. Can anyone of you explain me how ...
3
votes
2answers
378 views

Bloom Filter for 208 million URLs

I need to create a bloom filter of 208 million URLs. What would be a good choice of bit vector size and number of hash functions? I tried a bit vector of size 1 GB and 4 hash functions, but it ...
4
votes
1answer
97 views

What is known about coRL and RL?

Wondering about any known relations between $\mathsf{RL}$ complexity class (one sided error with logarithmic space) and its complementary class, $\mathsf{coRL}$. Are they the same class? What are ...
5
votes
2answers
110 views

An edge that connects more than two nodes in a graph?

Is there a way to create a single edge on a graph that connects 3 or more nodes? For example, let's say that the probability of Y occurring after X is 0.1, and the probability of Z occurring after Y ...
6
votes
1answer
124 views

Probabilistic poly-time machine always halts on all inputs?

In the usual definition of probabilistic poly-time machine it is said that the machine halts in polynomial time for all inputs. Is the intention really to say that the machine halts for all inputs, ...
7
votes
1answer
229 views

Probabilistic test of matrix multiplication with one-sided error

Given three matrices $A, B,C \in \mathbb{Z}^{n \times n}$ we want to test whether $AB \neq C$. Assume that the arithmetic operations $+$ and $-$ take constant time when applied to numbers from ...
3
votes
1answer
114 views

Randomized String Searching

I need to detect whether a binary pattern $P$ of length $m$ occurs in a binary text $T$ of length $n$ where $m < n$. I want to state an algorithm that runs in time $O(n)$ where we assume that ...
3
votes
2answers
119 views

Is the number of coin tosses of a probabilistic Turing machine a Blum complexity measure?

I read that the number of coin tosses of a probabilistic Turing machine (PTM) is not a Blum complexity measure. Why? Clarification: Note that since the execution of the machine is not deterministic, ...