Constant Amortized Time Enumeration of Eulerian trails
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In this paper, we consider enumeration problems for edge-distinct and vertex-distinct Eulerian trails. Here, two Eulerian trails are edge-distinct if the edge sequences are not identical, and they are vertex-distinct if the vertex sequences are not identical. As the main result, we propose optimal enumeration algorithms for both problems, that is, these algorithm runs in 𝒪(N) total time, where N is the number of solutions. Our algorithms are based on the reverse search technique introduced by [Avis and Fukuda, DAM 1996], and the push out amortization technique introduced by [Uno, WADS 2015].
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