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Enumerating Eulerian Trails via Hamiltonian Path Enumeration

  • Hiroyuki Hanada
  • Shuhei Denzumi
  • Yuma Inoue
  • Hiroshi Aoki
  • Norihito Yasuda
  • Shogo Takeuchi
  • Shin-ichi Minato
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8973)

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 Hamiltonian path in L(G) corresponds to an Eulerian 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.

Keywords

Eulerian trail Hamiltonian path path enumeration line graph zero-suppressed binary decision diagram 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Hiroyuki Hanada
    • 1
  • Shuhei Denzumi
    • 2
  • Yuma Inoue
    • 2
  • Hiroshi Aoki
    • 2
  • Norihito Yasuda
    • 1
  • Shogo Takeuchi
    • 1
  • Shin-ichi Minato
    • 1
    • 2
  1. 1.ERATO Minato Discrete Structure Manipulation System ProjectJapan Science and Technology AgencySapporoJapan
  2. 2.Graduate School of Information Science and TechnologyHokkaido UniversitySapporoJapan

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