Optimizing graph spectra for Subgraph Isomorphism Checking

Abstract

Solving subgraph isomorphism problem has emerged as a major part in study of graph mining, while its computational complexity is known to be NP-complete. To address this complexity issue, a subgraph isomorphism checking approach between two graphs has been assessed by applying Cauchy's Interlace theorem to symmetric matrices such as adjacency matrices representing the graphs because of its low computational complexity O(n3). However, the accuracy of this approach is known to be low, when we simply assign edge label IDs in the graphs to the elements of their adjacency matrices. In this paper, we propose a novel approach called OPTSPEC (OPTimized SPECtra for subgraph isomorphism checking) which optimizes a mapping from a substructure of graphs to an element of their adjacency matrices so as to maximize the effectiveness of Interlace theorem. We experimentally evaluated our approach by using artificial graph data, and confirmed the significant accuracy of its subgraph isomorphism checking.