Boltzmann sampling of irreducible context-free structures in linear time

We continue our program of improving the complexity of so-called ‘Boltzmann sampling’ algorithms, for the exact sampling of combinatorial structures, and reach average linear-time complexity, i.e. optimality up to a multiplicative constant. Here we solve this problem for ‘irreducible context-free structures’, a broad family of structures to which the celebrated Drmota–Lalley–Woods Theorem applies. Our algorithm is a ‘rejection algorithm’. The main idea is to single out some degrees of freedom, i.e. write p(x) = p1(y)p2(x|y), which allows to introduce a rejection factor at the level of the y object, that is almost surely of order 1.

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