二元de Bruijn序列的图连接贪婪算法
A Graph Joining Greedy Approach to Binary de Bruijn Sequences
摘要：
使用贪心算法生成de Bruijn序列是一种经典的方法，已经产生了许多有趣的理论结果。本文研究了一种算法，我们称之为广义的反序（G-O）。它包括所有以前的贪心算法，除了在de Bruijn图上应用的Fleury算法，作为具体实例。该算法在输入端有一对合适的反馈函数和初始状态时，可以产生任意复杂度至少为2的非线性二元周期序列。特别地，给出了该算法产生二进制de Bruijn序列的一个充要条件.这需要使用在其各自的状态图中具有唯一循环或回路的反馈函数。此外，我们讨论了对GPO算法的修改，以处理更多状态图具有多个循环或回路的反馈函数族。这些最终在一个图连接方法。几个大类的反馈函数，随后被用来说明如何在实践中的图形连接正反（GJPO）算法的改进的反演算法。
英文摘要：
Using greedy algorithms to generate de Bruijn sequences is a classical approach that has produced numerous interesting theoretical results. This paper investigates an algorithm which we call the Generalized Prefer-Opposite (GPO). It includes all prior greedy algorithms, with the exception of the Fleury Algorithm applied on the de Bruijn graph, as specific instances. The GPO Algorithm can produce any binary periodic sequences with nonlinear complexity at least two on input a pair of suitable feedback function and initial state. In particular, a sufficient and necessary condition for the GPO Algorithm to generate binary de Bruijn sequences is established. This requires the use of feedback functions with a unique cycle or loop in their respective state graphs. Moreover, we discuss modifications to the GPO Algorithm to handle more families of feedback functions whose state graphs have multiple cycles or loops. These culminate in a graph joining method. Several large classes of feedback functions are subsequently used to illustrate how the GPO Algorithm and its modification into the Graph Joining Prefer-Opposite (GJPO) Algorithm work in practice.
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