Seeded Graph Matching Via Joint Optimization of Fidelity and Commensurability

Given two graphs, the graph matching problem (GMP) seeks to find a correspondence (i.e., "matching") between the vertex sets that best preserves similar substructures across the graphs. The graph matching problem has applications across many diverse disciplines including document processing, mathematical biology, network analysis and pattern recognition, to name a few. Unfortunately, no graph matching algorithm is known to be efficient. Indeed, even the easier problem of matching isomorphic simple graphs is of famously unknown complexity (see [7]). Because of its practical applicability, there exist numerous approximate graph matching algorithms in the literature; for an excellent survey of the existing literature, see [4].