Approximate enumeration of self-avoiding walks

Algorithms for the approximate enumeration of lattice self-avoiding walks are reviewed. Innovations in the approximate counting of such walks started with the invention of PERM (the pruned enhanced Rosenbluth method) in 1997. The recent generalization of the underlying Rosenbluth method (RM) to the GARM (generalized atmospheric RM), and to the GAS (generalized atmospheric sampling) algorithm, opens up exciting new possibilities for the approximate enumeration of walks. The implementation and use of these algorithms are described, as are associated results, including numerical data that show that high-quality estimates of the number of walks can be obtained.