Entropic Generation of Binary Words
For algorithm designers needing efficient generation of combinatorial objects, this provides a nearly optimal method in terms of random bit usage.
The paper introduces a random bit recycling paradigm to generate binary words of fixed Hamming weight, achieving linear time and near-optimal random bit consumption that matches the Shannon entropic lower bound.
The uniform generation of k Hamming weight binary words, equivalent to sampling k-subsets from n elements, relies on random bits, which can be expensive. We introduce a novel paradigm, random bit recycling, and use it to generate such binary words in linear time while consuming as few random bits as possible. The resulting algorithm is nearly optimal in terms of random bit consumption, meaning that it closely matches the Shannon entropic lower bound coming from information theory.