Constant amortized time enumeration of Eulerian trails

Abstract

In this paper, we consider enumeration problems for edge-distinct and vertex-distinct Eulerian trails. Two Eulerian trails are said to be edge-distinct if the edge sequences are not identical, and they are said to be vertex-distinct if the vertex sequences are not identical. To solve these problems, we propose optimal enumeration algorithms that run in O(N+m) total time, where N is the number of solutions and m is the number of edges in an input connected graph. The proposed 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].