Complementary algorithms for graphs and percolation
Abstract
A pair of complementary algorithms are presented. One of the pair is a fast method for connecting graphs with an edge. The other is a fast method for removing edges from a graph. Both algorithms employ the same tree-based graph representation and so, in concert, can arbitrarily modify any graph. Since the clusters of a percolation model may be described as simple connected graphs, an efficient Monte Carlo scheme can be constructed which uses the algorithms to sweep the occupation probability back and forth between two turning points. This approach concentrates computational sampling time within a region of interest. A high-precision value of pc=0.59274603(9) was thus obtained, by Mersenne twister, for the two-dimensional square site percolation threshold.
- Publication:
-
Physical Review E
- Pub Date:
- August 2007
- DOI:
- arXiv:
- arXiv:0708.0600
- Bibcode:
- 2007PhRvE..76b7702L
- Keywords:
-
- 02.70.-c;
- 02.10.Ox;
- 05.10.Ln;
- 64.60.Ak;
- Computational techniques;
- simulations;
- Combinatorics;
- graph theory;
- Monte Carlo methods;
- Renormalization-group fractal and percolation studies of phase transitions;
- Computer Science - Data Structures and Algorithms;
- J.2.x;
- I.6.8
- E-Print:
- 5 pages, 3 figures, poster version presented at statphys23 (2007)