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Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
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A practical approach to Morse-Smale complex computation: scalability and generality.

Attila Gyulassy1, Peer-Timo Bremer, Bernd Hamann

  • 1UC Davis and Lawrence Livermore National Laboratory. aggyulassy@ucdavis.edu

IEEE Transactions on Visualization and Computer Graphics
|November 8, 2008
PubMed
Summary

We present a new algorithm for computing Morse-Smale (MS) complexes, enabling efficient feature extraction from large-scale data. This method works on various mesh types and simplifies computation on standard hardware.

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Area of Science:

  • Computational topology
  • Data visualization
  • Scientific computing

Background:

  • Morse-Smale (MS) complexes are valuable for scalar data analysis.
  • Efficient computation of MS complexes for large datasets is a significant challenge.
  • Existing methods struggle with scalability and diverse data structures.

Purpose of the Study:

  • To develop a scalable and extensible framework for computing MS complexes.
  • To enable efficient topological analysis of large-scale data on commodity hardware.
  • To handle diverse mesh types including grids, simplicial, and adaptive multiresolution (AMR) meshes.

Main Methods:

  • A novel divide-and-conquer algorithm for memory-efficient MS complex computation.
  • On-the-fly simplification to control output size.
  • Support for various data formats and implementation-specific optimizations.
  • Complete characterization of critical point cancellations in arbitrary dimensions.

Main Results:

  • A new framework for computing MS complexes on large-scale data of any dimension.
  • Demonstration of memory-efficient computation on diverse mesh types.
  • Successful computation of a 1 billion node grid MS complex on a laptop with 2GB memory.
  • Characterization of critical point cancellations enabling topology-based analysis.

Conclusions:

  • The developed framework significantly advances the computation of MS complexes for large datasets.
  • Enables topology-based analysis of massive data on standard computers.
  • The approach is versatile, supporting various data structures and offering memory efficiency.