Random Graph Generation in Context-Free Graph Languages

TL;DR

This paper introduces a method for uniformly generating random hypergraphs within context-free hypergraph languages by adapting string grammar algorithms, achieving quadratic time complexity for non-ambiguous cases.

Contribution

It adapts Mairson's string grammar generation algorithm to hyperedge replacement grammars, enabling uniform random hypergraph generation efficiently.

Findings

Generates hypergraphs uniformly at random for non-ambiguous grammars

Achieves quadratic time complexity in hypergraph generation

Demonstrates approach with a term graph example

Abstract

We present a method for generating random hypergraphs in context-free hypergraph languages. It is obtained by adapting Mairson's generation algorithm for context-free string grammars to the setting of hyperedge replacement grammars. Our main results are that for non-ambiguous hyperedge replacement grammars, the method generates hypergraphs uniformly at random and in quadratic time. We illustrate our approach by a running example of a hyperedge replacement grammar generating term graphs.