TCS-TR-A-14-79

Date: Thu Oct 9 18:09:11 2014

Title: Enumerating Eulerian Trails Based on Line Graph Conversion

Authors: Hiroyuki Hanada, Shuhei Denzumi, Yuma Inoue, Hiroshi Aoki, Norihito Yasuda, Shogo Takeuchi and Shin-ichi Minato

Contact:

First name: Shin-ichi
Last name: Minato
Address: Graduate School of Information Science and Technology, Hokkaido University, North 14 West 9, Sapporo, 060- 0814, Japan
Email: minato@ist.hokudai.ac.jp

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.