Constant Amortized Time Enumeration of Eulerian trails
Data Structures and Algorithms
2023-01-24 v1
Abstract
In this paper, we consider enumeration problems for edge-distinct and vertex-distinct Eulerian trails. Here, two Eulerian trails are \emph{edge-distinct} if the edge sequences are not identical, and they are \emph{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 total time, where 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].
Keywords
Cite
@article{arxiv.2101.10473,
title = {Constant Amortized Time Enumeration of Eulerian trails},
author = {Kazuhiro Kurita and Kunihiro Wasa},
journal= {arXiv preprint arXiv:2101.10473},
year = {2023}
}