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Questions tagged [streaming]

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6 votes
2 answers
232 views

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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  • 63
6 votes
0 answers
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 ...
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4 votes
1 answer
78 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 ...
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  • 574
5 votes
1 answer
151 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 \...
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  • 11k
4 votes
0 answers
239 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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  • 9,358
18 votes
2 answers
789 views

Bounds on the size of the smallest NFA for L_k-distinct

Consider the language $L_{k-distinct}$ consisting of all $k$-letter strings over $\Sigma$ such that no two letters are equal: $$ L_{k-distinct} :=\{w = \sigma_1\sigma_2...\sigma_k \mid \forall i\in[k]...
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  • 9,358
0 votes
1 answer
84 views

"Computing on data streams" clarification

In the 1998 technical note "Computing on data streams" by Monika Rauch Henzinger , Prabhakar Raghavan , Sridar Rajagopalan (found here: http://www.eecs.harvard.edu/~michaelm/E210/datastreams.pdf) ...
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  • 113
3 votes
0 answers
374 views

Streaming Algorithm Lower Bounds by Communication Complexity

I am learning the methods for proving lower bounds on streaming algorithms using communication complexity. My question is about a basic technique to prove lower bounds on streaming models using the ...
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  • 549
7 votes
1 answer
910 views

Streaming Algorithms: Motivations for estimating frequency moments

The celebrated AMS paper "The space complexity of approximating the frequency moments" defines the problem as following: Let $a_1, a_2,\dotsc, a_m$ be a sequence of integers where each $a_j \in \{1,2,...
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  • 395
0 votes
1 answer
158 views

Functions and Counting Problems in Streaming Computation

I have read a stream computation paper in STOC07(Paul Beame, T. S. Jayram, and Atri Rudra. Lower bounds for randomized read/write stream algorithms.) and FOCS08(Paul Beame and Trinh Huynh. On the ...
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  • 317
4 votes
1 answer
262 views

What's the strict definition of random coins in streaming algorithm?

I have a very basic question about random bits in streaming. How could a streaming algorithm use them? Can the algorithm use the same random bit at the start of the execution and look at it again ...
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  • 331
5 votes
1 answer
266 views

Why does deterministic recognition of DYCK(2) languages in the streaming model take linear space?

I was reading the paper "Recognizing Well-Paranthesized Expressions in the Streaming Model" by Magniez, Mathieu and Nayak where they give upper and lower bounds on the space required to recognize DYCK(...
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12 votes
3 answers
462 views

Streaming derandomization

Stream algorithms require randomization for the most part to do anything nontrivial, and because of the small-space constraint, need PRGs that use little space. I know of two methods that have been ...
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