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Faster heuristics for graph burning.

Rahul Kumar Gautam1, Anjeneya Swami Kare1, Durga Bhavani S1

  • 1School of Computer and Information Sciences, University of Hyderabad, Hyderabad, India.

Applied Intelligence (Dordrecht, Netherlands)
|November 12, 2021
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Summary
This summary is machine-generated.

This study introduces three new heuristics for the graph burning problem, a method for efficient network information spreading. These novel algorithms, BBGH, ICCH, and CBRH, offer faster and simpler solutions for determining optimal information dissemination sequences.

Keywords:
Burning numberGraph burningHeuristic

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Area of Science:

  • Network Science
  • Computer Science
  • Graph Theory

Background:

  • Graph burning involves spreading information through a network in discrete steps.
  • The goal is to find an optimal sequence of nodes to minimize the time for complete network coverage.
  • The graph burning problem is NP-Hard, necessitating efficient approximation algorithms and heuristics.

Purpose of the Study:

  • To propose three novel heuristics for the graph burning problem: Backbone Based Greedy Heuristic (BBGH), Improved Cutting Corners Heuristic (ICCH), and Component Based Recursive Heuristic (CBRH).
  • To address the challenges of graph burning on disconnected graphs, particularly relevant for large, real-world networks.
  • To evaluate the performance and efficiency of the proposed heuristics against existing approximation algorithms.

Main Methods:

  • Developing BBGH: Identifies a network backbone and greedily selects vertices from it for burning.
  • Developing ICCH: Employs a shortest path approach, selecting central nodes for burning.
  • Developing CBRH: A component-aware heuristic designed to effectively handle disconnected graphs by prioritizing components.

Main Results:

  • The proposed heuristics, BBGH, ICCH, and CBRH, were implemented and tested on various benchmark and large-scale networks (over 50K nodes).
  • Experimental results demonstrate that the new heuristics are significantly faster and simpler to implement compared to existing methods.
  • CBRH shows particular effectiveness on disconnected graphs, a common scenario in practical network analysis.

Conclusions:

  • The developed heuristics provide efficient and practical solutions for the NP-Hard graph burning problem.
  • These algorithms offer substantial improvements in terms of speed and implementation simplicity.
  • The component-based approach in CBRH is crucial for effectively managing information spread in disconnected networks.