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Linear Time Vertex Partitioning on Massive Graphs.

Peter Mell1, Richard Harang2, Assane Gueye3

  • 1National Institute of Standards and Technology, USA.

International Journal of Computer Science (Rabat)
|June 24, 2016
PubMed
Summary
This summary is machine-generated.

We present a linear-time algorithm for vertex partitioning in massive graphs, improving upon existing methods for large-scale network analysis. This scalable solution efficiently handles graphs with millions of nodes, crucial for understanding complex network structures.

Keywords:
Vertex partitioninggraph cuts

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Area of Science:

  • Graph Theory
  • Network Science
  • Computer Science

Background:

  • Vertex partitioning to minimize largest component size is NP-complete.
  • Existing heuristics struggle with massive graphs due to high time complexity.

Purpose of the Study:

  • Develop a scalable algorithm for vertex partitioning on graphs with tens of millions of nodes.
  • Reduce the time complexity of iterative node removal heuristics.

Main Methods:

  • Employed a heuristic of iteratively removing the node of largest degree.
  • Developed a linear-time solution using an array indexed by node degree and hash tables.
  • Analyzed time and memory complexity, demonstrating linear scalability.

Main Results:

  • Achieved linear time complexity (O(n)) for the vertex partitioning heuristic.
  • Demonstrated linear memory usage, contrary to expectations for improved time complexity.
  • Empirically validated scalability on random graphs up to 15,000 nodes.
  • Successfully applied the method to a 34-million-node graph of internet router connectivity.

Conclusions:

  • The developed linear-time algorithm provides a tractable solution for vertex partitioning on massive graphs.
  • This approach significantly advances the analysis of large-scale networks, such as internet topology.