Random generation and enumeration of bipartite permutation graphs

Authors:
Toshiki Saitoh;Yota Otachi;Katsuhisa Yamanaka;Ryuhei Uehara
Affiliations:
ERATO, MINATO Discrete Structure Manipulation System Project, JST, North 14, West 9, Sapporo, Hokkaido 060-0814, Japan;Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan;Department of Electrical Engineering and Computer Science, Iwate University, Iwate 020-8550, Japan;School of Information Science, JAIST, Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan
Venue:
Journal of Discrete Algorithms
Year:
2012

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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 reverse search, and it outputs each connected bipartite permutation graph in O(1) time.