Towards a taxonomy of subgraph isomorphism algorithms

The study of algorithms which solve the subgraph isomorphism problem is very important because it has many applications where data is modelled as graphs. Despite the subgraph isomorphism problem being NP-hard, research has been dedicated to proposing new algorithms which are designed to improve the shortcomings of the algorithms that have been previously proposed. However, some of the newly invented solutions do not improve on their predecessors and some are redundant because their algorithmic properties are not different from some existing algorithms. The problem arises because minimal effort has been made towards organising subgraph isomorphism algorithms in terms of their relationships and differences such that new solutions utilise knowledge extracted from the organisation of knowledge about these algorithms. The need to organise information has motivated the current study to show how Formal Concept Analysis can be used to build a conceptlattice based taxonomy of algorithms. There are many subgraph isomorphism algorithms and it is not feasible to list all of them. As a result, the implications between the attributes of the algorithms are used to build a representative taxonomy of the domain of subgraph isomorphism algorithms. The paper focuses on how the tools from Formal Concept Analysis can be used to build a taxonomy. This is illustrated using a small sample subset of algorithms.