Date: Thu Oct 9 18:09:11 2014
Authors: Hiroyuki Hanada, Shuhei Denzumi, Yuma Inoue, Hiroshi Aoki, Norihito Yasuda, Shogo Takeuchi and Shin-ichi Minato
Abstract. Given an undirected graph G, we consider enumerating all Eulerian trails, that is, walks containing each of the edges in G just once. We consider achieving it with the enumeration of Hamiltonian paths with the zero-suppressed decision diagram (ZDD), a data structure that can efficiently store a family of sets satisfying given conditions. First we compute the line graph L(G), the graph representing adjacency of the edges in G. We also formulated the condition when a path in L(G) corresponds to a trail in G because every trail in G corresponds to a path in L(G) but the converse is not true. Then we enumerate all Hamiltonian paths in L(G) satisfying the condition with ZDD by representing them as their sets of edges.
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