Questions tagged [streaming-algorithms]

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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 $\pi, \pi, \cdots, \pi[n]$. The output should be the parity of ...
281 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 ...
597 views

Constraints on sliding windows

Let $L\subseteq \Sigma^*$ be a language of finite words and $n>0$ some integer. I would like to know if anything is known on the time and space complexity with respect to $n$ to check for ...
288 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 ...
189 views

Complexity class of efficient streaming algorithms

Consider the class of problems $\mathsf{StreamL}$ which can be solved in logarithmic space reading the input in a single pass from left to right. In other words: $L \in \mathsf{StreamL}$ if there ...
499 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: ...
920 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, ...
251 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-...
881 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 ...
168 views

Counting distinct elements in a stream with expiration

Counting the number of distinct elements in a stream is a well-known and studied problem in computer science, for example Flajolet-Martin algorithm. There are algorithms for calculating the number of ...
142 views

Estimating the cardinality of multisets given some sets of different sizes

The count-distinct problem is: given a stream of elements $x_1, \dots, x_n$ which contains duplicates, find the number of distinct elements using a small amount of space. I also want the following ...
147 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 ...
102 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 ...
150 views

70 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: ...
235 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 ...
126 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 ...
765 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 ...
173 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 ...