Asymptotically faster algorithm for counting self-avoiding walks and self-avoiding polygons

@article{Zbarsky2019AsymptoticallyFA,
  title={Asymptotically faster algorithm for counting self-avoiding walks and self-avoiding polygons},
  author={Samuel Zbarsky},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2019},
  volume={52}
}
  • Samuel Zbarsky
  • Published 11 March 2019
  • Computer Science
  • Journal of Physics A: Mathematical and Theoretical
We give an algorithm for counting self-avoiding walks or self-avoiding polygons of length n that runs in time on 2-dimensional lattices and time on d-dimensional lattices for d  >  2. 

Enumerative Combinatorics of Lattice Polymers

DOI: https://doi.org/10.1090/noti2255 physicists who appreciatemathematical beauty), the physicallymotivatedmodels aremathematically appealing, and have rich combinatorial structure. The third reason

The growth constant for self-avoiding walks on the fcc and bcc lattices

We extend a binary tree implementation of the pivot algorithm to the face-centered cubic and body-centered cubic lattices, and use it to calculate the growth constant, µ, for self-avoiding walks on

References

SHOWING 1-10 OF 16 REFERENCES

Exact enumeration of self-avoiding walks

A prototypical problem on which techniques for exact enumeration are tested and compared is the enumeration of self-avoiding walks. Here, we show an advance in the methodology of enumeration, making

Algebraic techniques for enumerating self-avoiding walks on the square lattice

The authors describe a new algebraic technique for enumerating self-avoiding walks on the rectangular lattice. The computational complexity of enumerating walks of N steps is of order 3N/4 times a

Generating functions for enumerating self-avoiding rings on the square lattice

It is shown that generating function techniques provide an efficient means of enumerating the number of self-avoiding rings (polygons) on the square lattice. The techniques can be applied to a number

A new transfer-matrix algorithm for exact enumerations: self-avoiding polygons on the square lattice

The new algorithm is used to extend the enumeration of polygons to length 130 from the previous record of 110 and shows significant improvement in the running time of the algorithm.

A new transfer-matrix algorithm for exact enumerations: self-avoiding walks on the square lattice

The new algorithm is used to extend the enumeration of self-avoiding walks to length 79 from the previous record of 71 and for metric properties, such as the average end-to-end distance, from 59 to 71.

Self-avoiding walk enumeration via the lace expansion

We introduce a new method for the enumeration of self-avoiding walks based on the lace expansion. We also introduce an algorithmic improvement, called the two-step method, for self-avoiding walk

Self-avoiding polygons on the square lattice

We have developed an improved algorithm that allows us to enumerate the number of self-avoiding polygons on the square lattice to perimeter length 90. Analysis of the resulting series yields very

Enumeration of self-avoiding walks on the square lattice

We describe a new algorithm for the enumeration of self-avoiding walks on the square lattice. Using up to 128 processors on a HP Alpha server cluster we have enumerated the number of self-avoiding

Exact enumeration of self-avoiding walks on BCC and FCC lattices

Self-avoiding walks on the body-centered-cubic (BCC) and face-centered-cubic (FCC) lattices are enumerated up to lengths 28 and 24, respectively, using the length-doubling method. Analysis of the

The self-avoiding walk Modern Birkhäuser Classics (New York: Springer) (reprint

  • original) S Zbarsky J. Phys. A: Math. Theor
  • 2013