Improving the Florentine algorithms: recovering algorithms for Motzkin and Schröder paths

02/16/2018

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by   Axel Bacher, et al.

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We present random sampling procedures for Motzkin and Schröder paths, following previous work on Dyck paths. Our algorithms follow the anticipated rejection method of the Florentine algorithms (Barcucci et al. 1994+), but introduce a recovery idea to greatly reduce the probability of rejection. They use an optimal amount of randomness and achieve a better time complexity than the Florentine algorithms.