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Questions tagged [streaming-algorithms]

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Precision Sampling for Heavy Hitters

This is an intermediate step to show that we can use precision sampling to estimate $l_1$ of a stream with help of heavy hitter. Say we have a bunch of random variables $u_i \sim \exp(1)$ for $i = 0, ...
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1answer
83 views

Reducing disjoint or indexing or inner-product problem to s-t connectivity problem in directed graph

I am asked to prove that an O(1)-pass randomized streaming algorithm that solves s-t connectivity problem in a simple directed graph $G=(V,E)$ with $|V|=n$ vertices, with sucess possibility $>\frac{...
4
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1answer
97 views

Sublinear finite-precision sampling in a stream

I am looking to sample a single item from a stream such that each item in the stream has an equal probability of being selected. This is a restricted version of the reservoir sampling problem. On a ...
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1answer
88 views

Estimate the maximum frequency of substring with given length in a very long character stream

Suppose there is a very long string $S\in \Sigma^N$ with length $N$, where $\Sigma$ is a relatively small alphabet (for example, $\Sigma=\{'a', 'b', \ldots, 'z'\}$). Now, given a budget $B$, the goal ...
6
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0answers
107 views

Framing the Count-Min Sketch as a Random Projection?

The count-min sketch data structure is used to estimate the frequencies of individual elements in a data stream. The authors note that the analysis of their data structure is simpler than other ...
3
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0answers
185 views

Streaming algorithms for sum

First of all, I am not sure whether this is a research level question. Please let me know if it is not. The question is about streaming algorithms for the sum of the given data stream. From ...
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0answers
129 views

Finding median in a changing array

Consider the problem of needing to support an $n$ integers array structure with two operations: Set(k,v) - set the $k$'th integer to value $v$ (i.e. $A[k]=v$). Median() - return the median value of ...
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0answers
91 views

Lower bounds for randomized frequency estimation algorithms

Consider a stream of elements $s_1s_2\ldots s_N$. A counter-based frequency estimation algorithm uses $m$ counters and is required to answer queries of the form "How many times did $x$ appear"? It ...
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59 views

Constructing a bad sequence for counter algorithm

Assume that we want to construct a sequence $s\in\{a,b\}^{N}$ such that $s$ contains exactly $n$ times the letter '$a$'. The sequence is then feed to the following probabilistic algorithm: ...
6
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3answers
704 views

Algorithm for finding heavy hitters in a weighted stream

The problem of finding heavy hitters in a stream is defined as follows: given a $N$ sized stream of elements, return a set $\mathcal D$, such that every item which arrived at least $N\theta$ times ...
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171 views

Integer queue summation

As part of a project I'm working on, we came up with an efficient algorithm for approximating the sum of an integers queue. The setting is as follows: Let $\epsilon>0$. we need to maintain a space-...
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0answers
67 views

Single-pass streaming quantile estimation using moments

Is it possible to estimate within $\epsilon$ the quantiles of a set of integers $\{x_1, x_2, \dots, x_n\}$ given only the values $\sum x_i^0,\sum x_i^1, \sum x_i^2, \dots, \sum x_i^{f(n)}$ where $f \...
3
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2answers
542 views

Sampling distinct values with probability proportional to their frequency

This is a variant of my previous question (Reservoir sampling of distinct values) I'm faced with a situation where I need to get m samples from a data stream (without replacement). Only one pass ...
7
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1answer
511 views

Reservoir sampling of distinct values

I'm faced with a situation where I need to get m samples from a data stream (without replacement). Only one pass through the data is possible. In my case, the stream contains many duplicate values, ...
8
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2answers
249 views

New Space Lower-Bound Techniques for Streaming Algorithms

Is communication complexity (CC) the only known approach for streaming algorithms lower bounds? Are there any other techniques, even if conditional lower bounds? In general, are we satisfied with the ...
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0answers
151 views

Reconstruction of sparse vectors from random matrices

In the paper [A], the following linear algebra result (Lemma 5 in [A]) is stated as being well known. Note that a vector is $s$-sparse if it contains at most $s$ non-zero entries. Lemma: Let $1 \...
15
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1answer
677 views

Computing parity of a permutation in a streaming-fashion way

I'm looking for a one-pass algorithm which computes parity of a permutation. I assume that an input permutation is given by stream $\pi[1], \pi[2], \cdots, \pi[n]$. The output should be the parity of ...
2
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2answers
211 views

Sketches, using ideal hash functions

I've been reading about sketches for processing streaming data (the CountMin sketch, the Count sketch, the tug-of-war sketch, FM sketches, etc.). They use hash functions that are required to be 2-...
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2answers
455 views

Streaming algorithms suitable for undergrad course

I am looking for interesting streaming algorithms that would be suitable for presentation in an undergraduate algorithms course. Good choices should probably satisfy the following requirements: ...
2
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0answers
102 views

Which paper to cite when referring to reservoir sampling *with replacement*?

As far as I can tell, the term "reservoir sampling" is commonly used to refer to sampling without replacement and references [1], [2], and [3] are cited while mentioning it. When referring to ...
4
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0answers
186 views

What is known about finding heavy hitters in a sliding window?

This question is strongly related to another question I asked here a few weeks ago. In this problem setting we have a stream of elements $s_1,s_2,...$, such that $\forall i: s_i\in \mathcal X$ for ...
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0answers
248 views

Additive error in counting the number of 1's in a sliding window?

The setting is as follows: We're given a stream of bits. At time $t$ you get to see bit $b_t$, and required to output $\widehat{s_t} \approx \Sigma_{i=0}^{N}b_{t-i}$ (i.e. approximately how many 1's ...