Random Generation and Enumeration of Bipartite Permutation Graphs

Authors:
Toshiki Saitoh;Yota Otachi;Katsuhisa Yamanaka;Ryuhei Uehara
Affiliations:
School of Information Science, JAIST, Ishikawa, Japan 923-1292;Department of Computer Science, Gunma University, Gunma, Japan 376-8515;Graduate School of Information Systems, The University of Electro-Communications, Tokyo, Japan 182-8585;School of Information Science, JAIST, Ishikawa, Japan 923-1292
Venue:
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Year:
2009

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Abstract

Connected bipartite permutation graphs without vertex labels are investigated. First, the number of connected bipartite permutation graphs of n vertices is given. Based on the number, a simple algorithm that generates a connected bipartite permutation graph uniformly at random up to isomorphism is presented. Finally an enumeration algorithm of connected bipartite permutation graphs is proposed. The algorithm is based on the reverse search, and it outputs each connected bipartite permutation graph in $\mbox{\cal O}(1)$ time.