# Questions tagged [streaming-algorithms]

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### Finding lightest k elements in data stream using small space

There has been much research and progress devoted towards algorithms for finding approximate $\ell_p$-Heavy Hitters with parameter $\epsilon$ in the streaming setting (For all 3 of the vanilla, ...
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### Universal Relation

In the paper Tight Bounds for Lp Samplers, Finding Duplicates in Streams, and Related Problems, the authors consider the universal relation problem in 2-party communication complexity, which is ...
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### How to show that the median cannot be maintained in $O(1)$ time?

Suppose that we have a stream of numbers $x_1,x_2,\ldots$ such that we wish to track the median of the values observed so far. This task is easy to do with $O(\log n)$ update time (where $n$ is the ...
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### 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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1 vote
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### 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 ...
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### 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 ...
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### 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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181 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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### 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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### 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: ...
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### 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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277 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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### 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 ...
312 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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### 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: ...
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### 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 ...
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### 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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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 ...