COMP9313 (20T2) ASSIGNMENT 1
Due at 20:59:59 2nd AUG, 2020 (Wed) Sydney Time
Q1. HDFS (30 Marks)
Let N be the number of DataNodes and R be the total number of blocks in the
DataNodes.
Assume the replication factor is 5, and k out of N DataNodes have failed
simultaneously.
1. Write down the formula of Li(k,N) for i ∈ {1, . . . , 5}, where Li(k,N) is
the number of blocks that have lost i replicas.
2. Let N = 500, R = 20, 000, 000, and k = 200. Compute the number of
blocks that cannot be recovered under this scenario. You need to show
both the steps and the final result to get full credit.
Q2. Spark (35 Marks)
Consider the following PySpark code snippet:
raw_data = [("Joseph", "Maths", 83), ("Joseph", "Physics", 74),
("Joseph", "Chemistry", 91), ("Joseph", "Biology", 82),
("Jimmy", "Maths", 69), ("Jimmy", "Physics", 62),
("Jimmy", "Chemistry", 97), ("Jimmy", "Biology", 80),
("Tina", "Maths", 78), ("Tina", "Physics", 73),
("Tina", "Chemistry", 68), ("Tina", "Biology", 87),
("Thomas", "Maths", 87), ("Thomas", "Physics", 93),
("Thomas", "Chemistry", 91), ("Thomas", "Biology", 74)]
rdd_1 = sc.parallelize(raw_data)
rdd_2 = rdd_1.map(lambda x:(x[0], x[2]))
rdd_3 = rdd_2.reduceByKey(lambda x, y:max(x, y))
rdd_4 = rdd_2.reduceByKey(lambda x, y:min(x, y))
rdd_5 = rdd_3.join(rdd_4)
rdd_6 = rdd_5.map(lambda x: (x[0], x[1][0]+x[1][1]))
rdd_6.collect()
1. Write down the expected output of the above code snippet.
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2. List all the stages in the above code snippet.
3. What makes the above implmentation inefficient? How would you modify
the code and improve the performance?
Q3: LSH (35 marks)
Consider a database of N = 1, 000, 000 images. Each image in the database is
pre-processed and represented as a vector o ∈ Rd. When a new image comes as
a query, it is also processed to form a vector q ∈ Rd. We now want to check if
there is any duplicates or near duplicates of q in the database. Specifically, an
image o is a near duplicate to q if cos(θ(o, q)) ≥ 0.9. We want to find any near
duplicate with probability no less than 99%.
We now design an LSH scheme using SimHash to generate candidate near
duplicates. Assume that for query q, there are 100 images that are near duplicate
to q.
1. Assume k = 5, how many tables does the LSH scheme require (i.e., L) to
ensure that we can find any near duplicate with probability no less than
99%?
2. Consider image o with cos(θ(o, q)) < 0.8, k = 5 and L = 10. What is the
maximum value of the probability of o to become a false positive of query
q?
You need to show the intermediate steps along with the final result to get
full credit.
Submission
Please write down your answers in a file named ass1.pdf. You must write
down your name and student ID on the first page. You should typeset your
answers in LATEX or MS Word. We do not accept handwritten answers.
You can submit your file using the command:
give cs9313 ass1 ass1.pdf
Late Penalty. We DO NOT ACCEPT LATE SUBMISSIONS (0 mark if
you do not submit on time).
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