Abstract
Let G = (V,A) be an Eulerian directed graph with an arc-labeling. In this work we study the problem of finding an Eulerian circuit of lexicographically minimal label among all Eulerian circuits of the graph. We prove that this problem is NP-hard by showing a reduction from the Directed-Hamiltonian-Circuit problem.
If the labeling of the arcs is such that arcs going out from the same vertex have different labels, the problem can be solved in polynomial time. We present an algorithm to construct the unique Eulerian circuit of lexicographically minimal label starting at a fixed vertex. Our algorithm is a recursive greedy algorithm which runs in \({\mathcal O}\)(|A|) steps.
We also show an application of this algorithm to construct the minimal De Bruijn sequence of a language.
Partially supported by Programa Iniciativa Científica Milenio P01-005 and Fundación Andes.
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Moreno, E., Matamala, M. (2006). Minimal Eulerian Circuit in a Labeled Digraph. In: Correa, J.R., Hevia, A., Kiwi, M. (eds) LATIN 2006: Theoretical Informatics. LATIN 2006. Lecture Notes in Computer Science, vol 3887. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11682462_67
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DOI: https://doi.org/10.1007/11682462_67
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