https://github.com/hdelan/msc-hpc-final-project

In this project I implement a CUDA Lanczos method to approximate the matrix exponential. The matrix exponential is an important centrality measure for large, sparse graphs.
https://github.com/hdelan/msc-hpc-final-project

cuda graph-algorithms krylov-methods

Last synced: about 1 year ago
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In this project I implement a CUDA Lanczos method to approximate the matrix exponential. The matrix exponential is an important centrality measure for large, sparse graphs.

• Host: GitHub
• URL: https://github.com/hdelan/msc-hpc-final-project
• Owner: hdelan
• Created: 2021-06-16T09:42:37.000Z (almost 5 years ago)
• Default Branch: master
• Last Pushed: 2021-09-16T21:11:02.000Z (over 4 years ago)
• Last Synced: 2025-04-12T22:44:14.333Z (about 1 year ago)
• Topics: cuda, graph-algorithms, krylov-methods
• Language: Cuda
• Homepage:
• Size: 68.7 MB
• Stars: 1
• Watchers: 1
• Forks: 0
• Open Issues: 1
• Metadata Files:
  • Readme: README.md

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README

          
# A CUDA Lanczos Method to Compute Graph Centrality

  

In the analysis of networks it is of great importance to identify central and non-central nodes. There are countless ways of measuring the centrality of nodes in a network, all with slightly different interpretations of what it means to be central. 

The aim of this project is to compute the centrality of nodes in an undirected graph  using the exponential matrix function: 

 

 will be approximated without forming   explicitly, instead using Krylov subspace methods, most notably the Lanczos method. This makes computing  scalable to the limits of the memory hardware, which are tested in this project. 

This project computes  both in serial and in parallel using CUDA.

## Report

The accompanying report can be found at ```writeup.pdf```.

## Data

In order to run code, data must be downloaded from:

https://drive.google.com/drive/folders/1HdyMdnjphMtafk8TBbWc0L-2V4OeWlmj?usp=sharing

and untarred. Please move the ```data/``` file (extracted from ```data.tar```) in this root directory.

## Implementations

There are many implementations of the Lanczos method in this project directory:

  - A serial method. See ```serial/README.md```

  - A CUDA method using on-card multiplication. See ```parallel-mult-on-card/README.md```

  - A CUDA method using two cards. See ```parallel-two-cards/README.md```

  - A final CUDA implementation. Which uses a CUDA Lanczos method, and a multithreaded CBLAS multOut routine. See ```parallel-final/README.md```

All directories except ```final``` include tests that check the accuracy of the method and of kernels.

Each implementation has its own ```lib/``` with slightly different code implementations. The final version of code can be found in ```parallel-final/lib```.

All code found in ```parallel-*``` directories must be run on a CUDA-enabled device.