# Complementary algorithms for graphs and percolation

@article{Lee2007ComplementaryAF, title={Complementary algorithms for graphs and percolation}, author={Michael J. Lee}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2007}, volume={76 2 Pt 2}, pages={ 027702 } }

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…

## 26 Citations

### Transfer matrix computation of generalized critical polynomials in percolation

- Mathematics
- 2012

Percolation thresholds have recently been studied by means of a graph polynomial PB(p), henceforth referred to as the critical polynomial, that may be defined on any periodic lattice. The polynomial…

### On the metric distortion of nearest-neighbour graphs on random point sets

- Mathematics, Computer ScienceArXiv
- 2008

An improved upper bound of 188 on the value of k_c(2) is presented, showing that if $k \geq 188$ the infinite cluster of $\NN(2,k)$ has an infinite subset of points with the property that the distance along the edges of the graphs between these points is at most a constant multiplicative factor larger than their Euclidean distance.

### Percolation transitions in two dimensions.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2008

The amplitude of the power-law correction associated with X_{t2}=4 is found to be dependent on the orientation of the lattice with respect to the cylindrical geometry of the finite systems.

### Postprocessing techniques for gradient percolation predictions on the square lattice.

- Computer Science, MathematicsPhysical review. E
- 2021

This work concludes that, due to skewness in the distribution of occupation probabilities visited the average does not converge monotonically to the true percolation threshold, and identifies several alternative metrics which do exhibit monotonic convergence and document their observed convergence rates.

### Percolation of aligned rigid rods on two-dimensional square lattices.

- Materials SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2012

The results show that the percolation threshold exhibits a decreasing function when it is plotted as a function of the kmer size, and in the case of aligned kmers, the intersection points of the curves of R(L,k)(p) for different system sizes exhibit nonuniversal critical behavior, varying continuously with changes in the kmers size.

### Sparse power-efficient topologies for wireless ad hoc sensor networks

- Computer Science2010 IEEE International Symposium on Parallel & Distributed Processing (IPDPS)
- 2010

The guiding insight of this work is that unlike an ad hoc wireless network, a wireless ad hoc sensor network does not require full connectivity among the nodes, as long as the sensing region is well covered by connected nodes, the network can perform its task.

### Nonmonotonic size dependence of the critical concentration in 2D percolation of straight rigid rods under equilibrium conditions

- Materials Science
- 2012

Numerical simulations and finite-size scaling analysis have been carried out to study the percolation behavior of straight rigid rods of length k (k-mers) on two-dimensional square lattices. The…

### Conformal invariance in three dimensional percolation

- Mathematics
- 2015

The aim of the paper is to present numerical results supporting the presence of conformal invariance in three dimensional statistical mechanics models at criticality and to elucidate the geometric…

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