COMPSCI 753 Algorithms for Massive Data
Assignment 2: Data Stream Algorithms
1 Assignment problem (50 pts)
The assignment aims at investigating data stream algorithms, including Reservoir Sampling, Misra-Gries Summary, and CountMin Sketch on real-world data sets.
In the assignment, you write a program1
to find frequent items on a stream. We use
the same data set from Assignment 1, i.e. the KOS blog entries data set for this
The file has the format: docID wordID count, where docID is the document ID,
wordID is the word ID in the vocabulary, and count is the word frequency. Ignoring the first 3 lines, we consider each line as a stream tuple (docID, wordID, count). In
the assignment, we do not use the information of count. This means that you can think
of count = 1 for each line. We want to find the most frequent words in our data set by
our data stream algorithms.
Students are encouraged to run your implementations on larger data sets, such as NYTimes news article and PubMed abstracts.
The assignment tasks and its point are as follows.
1. Execute bruteforce computation (10 pts): Compute the frequency vector of
all words, descendingly sort the words by their frequencies, and save the result
into file (since you might use the bruteforce result for the next tasks). You need
(a) The average frequency of the words in stream (5 pts).
(b) Plot the sorted frequency of words to observe the skewed distribution (5 pts).
2. Reservoir Summary (10 pts): Implement Reservoir Sampling to see the skewed
distribution of our frequency vector. Fix the summary size S = 10, 000, you need
(a) Estimate the frequency vector from our Reservoir Summary, and
plot this estimate vector to see the approximation skewness (5 pts).
(b) Run your Reservoir Sampling 5 times and report the average number of times the summary has been updated over these 5 runs (5
3. Misra-Gries Summary (15 pts): Implement Misra-Gries summary to find the
most frequent words whose frequency is larger than 1,000. You need to:
1no restriction on programming languages used but preferred Python.
(a) Explain the size of summary you choose such that you can find
these frequent words (5 pts).
(b) Run your Misra-Gries summary and report the number of decrement steps with your chosen parameter (10 pts).
4. CountMin Sketch (15 pts): Implement CountMin sketch to estimate the frequency of words. You need to:
(a) Explain the size of summary you choose such that the estimate
error is at most 100 (5 pts).
(b) Run your CountMin Sketch with your chosen parameters, and report the estimate of the frequency of the words, whose frequency
is larger than 1,000 found in the bruteforce algorithm (10 pts).
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