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Using greedy algorithms to generate de Bruijn sequences is a classicalapproach that has produced numerous interesting theoretical results. This paperinvestigates an algorithm which we call the Generalized Prefer-Opposite (GPO).It includes all prior greedy algorithms, with the exception of the FleuryAlgorithm applied on the de Bruijn graph, as specific instances. The GPOAlgorithm can produce any binary periodic sequences with nonlinear complexityat least two on input a pair of suitable feedback function and initial state.In particular, a sufficient and necessary condition for the GPO Algorithm togenerate binary de Bruijn sequences is established. This requires the use offeedback functions with a unique cycle or loop in their respective stategraphs. Moreover, we discuss modifications to the GPO Algorithm to handle morefamilies of feedback functions whose state graphs have multiple cycles orloops. These culminate in a graph joining method. Several large classes offeedback functions are subsequently used to illustrate how the GPO Algorithmand its modification into the Graph Joining Prefer-Opposite (GJPO) Algorithmwork in practice.

A Graph Joining Greedy Approach to Binary de Bruijn Sequences