CSC4760 Assignment 2 Solved

1.  (PageRank)

Dataset:

The toy dataset is the following graph. The PageRank values are already known. We can use it to check your program.

Figure 1: A toy graph for computing PageRank. The number on the edge represents the transition probability from one node to another.

The PageRank values are given in the following table (given that the decay factor 𝑐𝑐 = 0.85):

PageRank:

Compute the PageRank value of each node in the graph. Please refer to the slides for more details about the PageRank method. The key PageRank equation is as follows.

⊤
𝐫𝐫=𝑐𝑐𝐏𝐏 𝐫𝐫+(1−𝑐𝑐)𝟏𝟏/𝑛𝑛

where 𝐫𝐫 represents the 𝑛𝑛 × 1 PageRank vector with each element 𝐫𝐫𝑖𝑖 representing the PageRank value of node 𝑖𝑖, 𝑛𝑛 represents the number of nodes in the graph, 𝐏𝐏 represents the 𝑛𝑛 × 𝑛𝑛 transition

probability matrix with each element 𝐏𝐏𝑖𝑖,𝑗𝑗 = 𝑝𝑝𝑖𝑖,𝑗𝑗 = 𝑑𝑑1 representing the transition probability from 𝑖𝑖𝑖𝑖⊤

node 𝑖𝑖 to node 𝑗𝑗, 𝑑𝑑 represents the degree of node 𝑖𝑖, 𝐏𝐏 represents the transpose of 𝐏𝐏, 𝑐𝑐 ∈ (0,1) represents a decay factor, 𝟏𝟏 represents a 𝑛𝑛 × 1 vector of all 1’s, and 𝑛𝑛 represents the number of nodes in the graph.

Please see the slides for more details.

In this assignment, we set the decay factor 𝑐𝑐 = 0.85 and set the number of iterations to 30.

Implementation:

Design and implement a MapReduce program to compute the PageRank values.

You are encouraged to implement the PageRank algorithm from scratch without using the provided “PageRankIncomplete.java” file.

The provided “PageRankIncomplete.java” file is incomplete. It will help you start programming with Hadoop. You need to understand the existing code and basic structure in order to complete the file.

Example command:

hadoop jar PageRank.jar file:///home/rob/pagerank/01InitialPRValues.txt file:///home/rob/pagerank/02AdjacencyList.txt file:///home/rob/pagerank/output 30

Report:

Please write a report illustrating your experiments. You need to explain your basic idea about how to design the computing algorithm. You may add comments to the source code such that the source code can be read and understood by the graders.

In the report, you should include the answers to the following questions.

1) Explanation of the source code:

1.1) How is the Mapper function defined? Which kind of intermediate results are generated?

1.2) How is the Reducer function defined? How do you aggregate the intermediate results and get the final outputs?

1.3) Do you use a Combiner function? Why or why not?

2) Experimental Results

2.1) Screenshots of the key steps. For example, the screenshot for the outputs in the terminal when you run “Hadoop jar YourJarFile” command. It will demonstrate that your program has no bug.

2.2) Explain your results. Does your implementation give the exact PageRank values? How large are the errors?