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Complementary algorithms for graphs and percolation.

Michael J Lee¹

¹Department of Physics and Astronomy, University of Canterbury, Christchurch, New Zealand.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|October 13, 2007

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New algorithms efficiently modify graphs, enabling precise calculation of the 2D square site percolation threshold (p(c)) at 0.59274603(9). This method optimizes computational sampling for percolation models.

Area of Science:

Computational physics
Graph theory
Statistical mechanics

Background:

Percolation models are crucial for understanding connectivity in various systems.
Efficient simulation methods are needed to accurately determine critical thresholds.

Purpose of the Study:

To introduce a pair of complementary algorithms for graph modification.
To develop an efficient Monte Carlo scheme for percolation threshold determination.

Main Methods:

A tree-based graph representation is utilized for fast edge addition and removal.
A Monte Carlo scheme sweeps occupation probability between turning points.

Main Results:

The algorithms enable arbitrary graph modification.

Related Experiment Videos

A high-precision value for the 2D square site percolation threshold was obtained: p(c) = 0.59274603(9).

Conclusions:

The developed algorithms and Monte Carlo scheme provide an efficient method for studying percolation.
This approach significantly enhances computational sampling efficiency in a region of interest.