Logic Programming with Graph Automorphism: Integratingnautywith Prolog (Tool Description)

Abstract

This paper presents the pl-nauty library, a Prolog interface to the nauty graph-automorphism tool. Adding the capabilities of nauty to Prolog combines the strength of the "generate and prune" approach that is commonly used in logic programming and constraint solving, with the ability to reduce symmetries while reasoning over graph objects. Moreover, it enables the integration of nauty in existing tool-chains, such as SAT-solvers or finite domain constraints compilers which exist for Prolog. The implementation consists of two components: pl-nauty, an interface connecting nauty's C library with Prolog, and pl-gtools, a Prolog framework integrating the software component of nauty, called gtools, with Prolog. The complete tool is available as a SWI-Prolog module. We provide a series of usage examples including two that apply to generate Ramsey graphs. This paper is under consideration for publication in TPLP.

Flexible Graph Matching and Graph Edit Distance Using Answer Set Programming

“…The lower bound of the complexity of graph isomorphism is a well-known open problem [4], but subgraph isomorphism and graph edit distance are NP-complete [11]. A number of practical algorithms for graph isomorphism have been studied, however, including NAUTY [17], which has also been integrated with Prolog [9]. However, most such algorithms consider graphs with vertex labels but not edge labels or properties, so are not directly applicable to property graph isomorphism.…”

Resolution with Symmetry Rule applied to Linear Equations

“…Therefore isomorphism solvers such as nauty/traces [13], which are highly efficient in practice, can be used to find the symmetries (see [6]). Symmetry detection is one of the standard applications of graph isomorphism solvers, for example there is a tool integrating nauty into Prolog [9] for this purpose.…”