In this project, we implemented the following versions of computing PageRank values:
- Simple Computation of PageRank.
- Jacobi Blocked Computation of PageRank.
- [Extra credit] Gauss-Seidel Computation of PageRank
- [Extra credit] Random Block Partition
The netID used to compute rejectMin and rejectLimit is gk256 with the reversed value being 0.652. The rejectMin is 0.5868 and the rejectLimit is 0.5968. In total, 7,524,304 out of 7,600,595 edges are selected in the graph, so we removed approximately 1% of the total edges. The pre-filtered edges file is stored in our S3 bucket: https://s3-us-west-2.amazonaws.com/edu-cornell-cs-cs5300s16-gk256/processed_edges.txt. To download the file, type aws s3 cp s3://edu-cornell-cs-cs5300s16-gk256/processed_edges.txt <target_file_name> in the terminal. It's the same format as the given edges.txt, i.e, src-node-number dest-node-number floating number.
The Python code used for filtering is in preprocess/process_edges.py. To run it, cd to the directory where process_edges.py is, put edges.txt in the same directory, then run python process_edges.py <input-file> <output-file>.
Additionally, we processed the edge file into a node-centric one so that it can be an appropriate input for mapper. It's also stored in our S3 bucket: https://s3-us-west-2.amazonaws.com/edu-cornell-cs-cs5300s16-gk256/nodepairs.txt. The format of a node entry is nodeID-blockID pagerank-value neighborNodeID-blockID [...]. To download the file, type aws s3 cp s3://edu-cornell-cs-cs5300s16-gk256/nodepairs.txt <target_file_name> in the terminal. Although some edges were rejected in the filtering, all the nodes in these edges were still retained.
The python code for this is in preprocess/process_nodes.py. To run it, cd to the directory where process_nodes.py is, put blocks.txt and the filtered edge file in the same directory, then run python process_nodes.py <edge-file> <block-file> <output-file>. You may find blocks.txt in data/.
To compute a bad partition for the graph, we assigned a node to a block based on the value of nodeID % totalBlocks where totalBlcoks is 68. This ensures that blocks are uniformly sized. The processed file is store in the S3 bucket as well:https://s3-us-west-2.amazonaws.com/edu-cornell-cs-cs5300s16-gk256/nodepairsRandom.txt. To download the file, type aws s3 cp s3://edu-cornell-cs-cs5300s16-gk256/nodepairsRandom.txt <target_file_name> in the terminal.
The python code for this is in preprocess/process_nodes_random.py. To run it, cd to the directory where process_nodes_random.py is, put the filtered edge file in the same directory, then run python process_nodes_random.py <edge-file> <block-file> <output-file>.
src/proj2/main/node/Node.java:
- Includes meta data about a node to make extracting information easier: nodeID-blockID, nodeID, blockID, currentPageRank, degree, emittedPageRank, and an array of destination nodes
- Please include this file when compling code Blocked or Gauss-Seidel Computation
src/proj2/main/util/Constants.java:
- Defines constant values used in this project, including damping factor, total node number, total block number, pass number for simple computation, convergence threhold, and enumerations for Hadoop counters
- Please include this file when compling code for every version of computation
Official jar files downloaded from Hadoop distribution
- hadoop/share/hadoop/common/hadoop-common-2.7.2.jar
- hadoop/share/hadoop/mapreduce/hadoop-mapreduce-client-core-2.7.2.jar
In case the submitted source code cannot be compiled, we exported a jar file for the project and included it in the submission. To run a certain version, for example, type hadoop jar <jar-file> proj2.main.simple.SimplePageRank <input-path> <output path> in the terminal. You may add the number of MapReduce pass you want to run as the third argument after <output path>.
How to run:
Required files: nodepairs.txt (for METIS block partition) and nodepairsRandom.txt (for Random block partition) downloaded from our S3 bucket, see section 2 for instruction.
SimplePageRank
$ hadoop jar <jar-file> proj2.main.simple.SimplePageRank <input-path> <output-path> <number-of-passes (Optional)>
For example if I put the nodepairs.txt file on hdfs input, I can type: hadoop jar pagerank.jar proj2.main.simple.SimplePageRank input output 3
If the <number-of-passes> argument is not specified, 5 MapReduce passes will be run as default.
Jacobi BlockedPageRank
$ hadoop jar <jar-file> proj2.main.blocked.BlockedPageRank <input-path> <output-path> <number-of-passes (Optional)>
For example: hadoop jar pagerank.jar proj2.main.blocked.BlockedPageRank input output 3 to run 3 MapReduce passes.
If the <number-of-passes> argument is not specified, MapReduce will run until convergence. If user specifies more than required passes to convergence, it will stop when it converges.
Gauss-Seidel BlockedPageRank
$ hadoop jar <jar-file> proj2.main.gauss.GaussPageRank <input-path> <output-path> <number-of-passes (Optional)>
For example: hadoop jar pagerank.jar proj2.main.gauss.GaussPageRank input output 3 to run 3 MapReduce passes.
If the <number-of-passes> argument is not specified, MapReduce will run until convergence. If user specifies more than required passes to convergence, it will stop when it converges.
Random Block Partition
This can be run on both Jacobi and Gauss-Seidel Blocked PageRank, just simply change the input to nodepairsRandom.txt and run the same command for each algorithm you want to run.
Running on AWS EMR
First, upload the jar file to your S3 bucket, and then when creating steps, select the jar file from your bucket and input three parameters into the arguments. The first one should be the class name. For example, if you want to run blocked pagerank, you need to input proj2.main.blocked.BlockPageRank as the main class. The second argument is the input file, which is located at s3://edu-cornell-cs-cs5300s16-gk256/nodepairs.txt. And the third is the output path, you can specify wherever you want in your S3 bucket. And there is a fourth optional paramter, which specify the maximum iteration in the page rank algorithm.
As an overall example, if you want to run Gauss Pagerank with maximum iteration 7, add proj2.main.blocked.BlockPageRank s3://edu-cornell-cs-cs5300s16-gk256/nodepairs.txt s3:\\{your s3 bucket output path} 7 as the input argument.
src/proj2/main/simple package:
- SimplePageRank.java
- Sets the input and output path accordingly
- Runs 5 MapReduce passes as default
- Initializes a MapReduce job for each MapReduce pass
- Computes per iteration average residual using a Hadoop Counter
- SimpleMapper.java
- Emits < srcNodeID-blockID, node entry > for computing residual and recovering node structure
- Emits < destNodeID-blockID, outgoingPageRank> for every outgoing edge
- SimpleReducer.java
- Updates the PageRank value for a node based on the PageRank values of its immediate neighbors, using the formula
(1-d)/N + d * sum (<PRt(u)/degree(u)>)where d = 0.85 and N = 685230 - Emits < nodeID-blockID, updated PageRank and reconstructed adjancency list >
- Adds the residual for this node |(PRt(u) - PRt+1(u))| / PRt+1(u) to a residual counter
- Updates the PageRank value for a node based on the PageRank values of its immediate neighbors, using the formula
The average residual errors in each MapReduce pass are as the following table. After 5 MapReduce passes, it's still far from convergence.
| Iteration | Average Error |
|---|---|
| 0 | 2.338036138444408 |
| 1 | 0.32297669467638457 |
| 2 | 0.19207763229971833 |
| 3 | 0.09406491742335128 |
| 4 | 0.06281398244773434 |
src/proj2/main/blocked package:
- BlockedPageRank.java
- Sets the input and output path accordingly
- Runs MapReduce passes until reaching convergence where the average relative residual error is below 0.001
- Computes average relative residual and average number of iterations per block for each reduce task by using two Hadoop Counters
- Reports the PageRank value for two lowest-numbered notes in each block after the entire computation converged
- BlockedMapper.java
- Emits < src-blockID, PR node entry > to compute residual in reducer and reconstruct node structure
- Emits < dest-blockID, BE srcNodeID-blockID destNodeID-blockID > for every destionation node in the same block as the source node
- Emits < dest-blockID, BC srcNodeID-blockID emittedPageRank destNodeID-blockID > for every destionation node not in the same block as the source node
- BlockedReducer.java
- Parse the input values and store in different HashMaps accordingly
- Performs in-block iterations until the in-block residual for the last iteration reaches convergence threshold 0.001
- Emits < nodeID-blockID, updated PageRank value and reconstructed adjancency list >
- Add the entire block reducer residual to a residual counter
- The relative residual error reflects the difference of a node's PageRank value before and after internal block iterations: |(PRstart(v) - PRend(v))| / PRend(v)
- Add the number of iterations in this block to an iteration counter
The average error and average in-block iteration number per block for each MapReduce pass of this version is as the following table. It shows that Jacobi Computation can reach convergence in 6 MapReduce passes while the Simple Computation would take longer.
| Iteration | Average Error | Average Number of Iterations per Block |
|---|---|---|
| 0 | 2.8105539255441174 | 17.529411764705884 |
| 1 | 0.037807487029411765 | 7.161764705882353 |
| 2 | 0.023995235897058823 | 5.882352941176471 |
| 3 | 0.009842906882352941 | 3.8970588235294117 |
| 4 | 0.003830367220588235 | 2.514705882352941 |
| 5 | 9.506281323529412E-4 | 1.338235294117647 |
The PageRank values for the two lowest-numbered nodes in each block are in result/jacobi_pagerank_values.txt
src/proj2/main/gauss package:
- GaussPageRank.java
- This is the same as the BlockedPageRank.java
- GaussMapper.java
- This is the same as the BlockedMapper.java
- GaussReducer.java
- Overall functionality is similar to
BlockedMapper.java(Jacobi version), including parse emitted output from Mapper, perform in-block iteration, and calculating in-block residual. However, in theiterateBlockOncemethod, instead of updating newPageRank values in the end of every iteration, it updates values right after the newPageRank is computed. And when summing up the incoming edges, we get the pageRank values from the newest one, instead of value before the in-block iteration loop, like what Jacobi did. Thus, by this approach we would be able to compute using updated pageRank values whenever possible. - We attempted Topological sort in order to compute even faster using the maximum differences between inDegree and outDegree for each node to handle cycle and isolated nodes (typically naive topological sort can only compute DAG graph). However, the pageRank computation converges in 9 passes, which is not valid, thus we didn't include it in the deliverables.
- Overall functionality is similar to
The average error and average in-block iteration number per block for each MapReduce pass of this version is as the following table:
| Iteration | Average Error | Average Number of Iterations per Block |
|---|---|---|
| 0 | 2.8109963380735294 | 9.308823529411764 |
| 1 | 0.03863734327941176 | 5.220588235294118 |
| 2 | 0.02519361007352941 | 4.544117647058823 |
| 3 | 0.010960004794117647 | 3.2941176470588234 |
| 4 | 0.004877597617647059 | 2.3823529411764706 |
| 5 | 0.00179155175 | 1.6176470588235294 |
| 6 | 7.902894411764706E-4 | 1.3088235294117647 |
The PageRank values for the two lowest-numbered nodes in each block are in result/gauss_pagerank_values.txt.
Comparison Jacobi vs Gauss-Seidel
The results show that Gauss-Seidel Computation takes less number of in-block iteration to converge, particularly for the first three MapReduce passes, and need one pass more than Jacobi to converge. The first pass improves average number of iterations per block by 47%, and the second pass improves by 27%. This satisfies the claim that by using the newest pageRank values whenever possible, the in-block pageRank converges faster.
| Iteration | Content | Jacobi METIS | Jacobi Random |
|---|---|---|---|
| 0 | Average error | 2.8105539255441174 | 2.3386830244264702 |
| 0 | Average iteration/block | 17.529411764705884 | 3.0 |
| 1 | Average error | 0.037807487029411765 | 0.32240249805882354 |
| 1 | Average iteration/block | 7.161764705882353 | 2.7205882352941178 |
| 2 | Average error | 0.023995235897058823 | 0.19121401836764707 |
| 2 | Average iteration/block | 5.882352941176471 | 2.0 |
| 3 | Average error | 0.009842906882352941 | 0.09338011023529412 |
| 3 | Average iteration/block | 3.8970588235294117 | 2.0 |
| 4 | Average error | 0.003830367220588235 | 0.0619256143382353 |
| 4 | Average iteration/block | 2.514705882352941 | 2.0 |
| 5 | Average error | 9.506281323529412E-4 | 0.03344842155882353 |
| 5 | Average iteration/block | 1.338235294117647 | 2.0 |
Compared to the result based on METIS, the Jacobi Computation based on a random partition converges much slower. Actually, it converges as slow as simple computation. This concludes that blockedPageRank only performs good in a good partition of block. It will have similar performance to SimplePageRank in a bad partitioned nodes, since the nodes will still be computed as node by node, in-block edges and boundary conditions are not reachable, the reducer will be getting a bunch of isolated in-blocks from the mapper.
| Iteration | Content | Gauss-Seidel METIS | Gauss-Seidel Random |
|---|---|---|---|
| 0 | Average error | 2.8109963380735294 | 2.3386887671911762 |
| 0 | Average iteration/block | 9.308823529411764 | 2.514705882352941 |
| 1 | Average error | 0.03863734327941176 | 0.32242048685294117 |
| 1 | Average iteration/block | 5.220588235294118 | 2.0294117647058822 |
| 2 | Average error | 0.02519361007352941 | 0.19124016294117646 |
| 2 | Average iteration/block | 4.544117647058823 | 2.0 |
| 3 | Average error | 0.010960004794117647 | 0.09341979076470588 |
| 3 | Average iteration/block | 3.2941176470588234 | 2.0 |
| 4 | Average error | 0.004877597617647059 | 0.062080906352941174 |
| 4 | Average iteration/block | 2.3823529411764706 | 2.0 |
| 5 | Average error | 0.00179155175 | 0.0335133024117647 |
| 5 | Average iteration/block | 1.6176470588235294 | 2.0 |
| 6 | Average error | 7.902894411764706E-4 | 0.026807231970588236 |
| 6 | Average iteration/block | 1.3088235294117647 | 2.0 |
The random partition performance for Gauss-Seidel is the same as random performance in Jacobi, that is, it has slow performance similar to SimplePageRank. This due to similar reason: in bad partitioned block, reducer will be getting a bunch of isolated in-blocks nodes without reachable in-block edges and boundary values. Thus, no matter what BlockPageRank algorithm we are using, for either Jacobi or Gauss-Seidel, blockPageRank only performs better in a good partitioned nodes.