Questions tagged [data-streams]

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7
votes
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223 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-...
6
votes
0answers
99 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 ...
5
votes
0answers
217 views

Why is HyperLogLog (near-)optimal?

The original HyperLogLog paper claims that this probabilistic counting algorithm is "near-optimal". The relevant section of the paper reads: Clearly, maintaining $\epsilon$-approximate counts till ...
4
votes
0answers
60 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: ...
4
votes
1answer
75 views

Does bisimulation or the approximation lemma work for monadic streams?

For ordinary streams $S_A := \nu X. A \times X$, there is a bisimulation lemma. It says that two streams are equal if there exists a bisimulation between them. A bisimulation is a relation $\sim$ on ...
3
votes
0answers
141 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 ...
2
votes
0answers
219 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 ...
2
votes
0answers
104 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 ...
2
votes
0answers
304 views

Simple to implement approximate quantile data structure for a stream of integers?

I'm looking for a simple data structure that will let me compute arbitrary approximate quantiles, within a percent or two error, on a stream of 64-bit integers (think of $n$ as being potentially as ...
1
vote
0answers
62 views

Sketching order statistics of a stream

Suppose we have a string stream over alphabet $[n]$. At each step, we would like to compute a sketch of the last $k$ elements, such that from the sketch we can approximate their relative order. For ...
1
vote
0answers
65 views

Bound the number of rounds in the sampling

Suppose we have a sequence $a_1,a_2,\ldots, a_n$, each $a_i$ is sampled uniformly and independently from $[0,1]$. Define $$ J_1=1,\\ \text{for}~i>1, ~J_i = 1 \iff a_i < \min \{a_1,a_2,...
0
votes
0answers
87 views

Questions on “Improved Sketching of Hamming Distance with Error Correcting” by Porat and Lipsky

What is the proof of lemma 4.3 in this paper? http://u.cs.biu.ac.il/~porately/papers/submission_24.pdf That is, how does it follow from 4.1 and 4.2? Also, why is the constant 8 necessary? How is it ...