Minimum Eulerian circuits and minimum de Bruijn sequences
نویسندگان
چکیده
منابع مشابه
Minimum Eulerian circuits and minimum de Bruijn sequences
Given a digraph (directed graph) with a labeling on its arcs, we study the problem of finding the Eulerian circuit of lexicographically minimum label. We prove that this problem is NP-complete in general, but if the labelling is locally injective (arcs going out from each vertex have different labels), we prove that it is solvable in linear time by giving an algorithm that constructs this circu...
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This paper presents a method to find new de Bruijn cycles based on ones of lesser order. This is done by mapping a de Bruijn cycle to several vertex disjoint cycles in a de Bruijn digraph of higher order and connecting these cycles into one full cycle. We characterize homomorphisms between de Bruijn digraphs of different orders that allow this construction. These maps generalize the well-known ...
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A (non-circular) de Bruijn sequence w of order n is a word such that every word of length n appears exactly once in w as a factor. In this paper, we generalize the concept to different settings: the multi-shift de Bruijn sequence and the pseudo de Bruijn sequence. An m-shift de Bruijn sequence of order n is a word such that every word of length n appears exactly once in w as a factor that start...
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A cycle is a sequence taken in a circular order—that is, follows , and are all the same cycle as . Given natural numbers and , a cycle of letters is called a complete cycle [1, 2], or De Bruijn sequence, if subsequences consist of all possible ordered sequences over the alphabet . In 1946, De Bruijn proved [1] (see [2]) that the number of complete cycles, under , is equal to . We propose the ov...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.11.027