Generating Outerplanar Graphs Uniformly at Random

We show how to generate labeled and unlabeled outerplanar graphs with n vertices uniformly at random in polynomial time in n. To generate labeled outerplanar graphs, we present a counting technique using the decomposition of a graph according to its block structure, and compute the exact number of labeled outerplanar graphs. This allows us to make the correct probabilistic choices in a recursive generation of uniformly distributed outerplanar graphs. Next we modify our formulas to count rooted unlabeled graphs, and finally show how to use these formulas in a Las Vegas algorithm to generate unlabeled outerplanar graphs uniformly at random in expected polynomial time. random structures, outerplanar graphs, efficient counting, uniform generation

• Type: Journal
• Year: 2006
• Where: CPC
• Authors: Manuel Bodirsky, Mihyun Kang
• Keywords: CPC 2006, Outerplanar Graphs, Polynomial Time, Unlabeled Outerplanar Graphs