## Testable Algorithms for Self-Avoiding Walks (1994)

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Citations: | 18 - 3 self |

### BibTeX

@MISC{Randall94testablealgorithms,

author = {Dana Randall and Alistair Sinclair},

title = {Testable Algorithms for Self-Avoiding Walks},

year = {1994}

}

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### Abstract

We present a polynomial time Monte Carlo algorithm for almost uniformly generating and approximately counting self-avoiding walks in rectangular lattices Z d . These are classical problems that arise, for example, in the study of long polymer chains. While there are a number of Monte Carlo algorithms used to solve these problems in practice, these are heuristic and their correctness relies on unproven conjectures. In contrast, our algorithm depends on a single, widely-believed conjecture that is weaker than preceding assumptions, and, more importantly, is one which the algorithm itself can test. Thus our algorithm is reliable, in the sense that it either outputs answers that are guaranteed, with high probability, to be correct, or finds a counter-example to the conjecture. 1 Summary 1.1 Background A self-avoiding walk in a graph is a walk which starts at a fixed origin and passes through each vertex at most once. This paper is concerned with self-avoiding walks in lattices, in par...