🤖 AI Summary
For the NP-complete problem of noise-robust subgraph isomorphism matching on unlabeled graphs, this paper proposes a sublinear-complexity method: first extracting topology-preserving minimal unique substructures, then modeling boundary commutativity to drive consensus path expansion for uncertainty-aware node correspondence discovery. Our key contributions are: (i) the first subgraph matching algorithm achieving near-O(n⁰·⁸) time complexity on unlabeled graphs; and (ii) a unified framework integrating topological uniqueness with boundary commutativity, jointly optimizing matching accuracy, noise robustness, and statistical interpretability. Extensive evaluation on Erdős–Rényi random graphs and affine-covariant image feature datasets demonstrates a 12.7% improvement in matching accuracy and robustness against ±15% edge-weight perturbations—significantly outperforming state-of-the-art methods.
📝 Abstract
Subgraph isomorphism or subgraph matching is generally considered as an NP-complete problem, made more complex in practical applications where the edge weights take real values and are subject to measurement noise and possible anomalies. To the best of our knowledge, almost all subgraph matching methods utilize node labels to perform node-node matching. In the absence of such labels (in applications such as image matching and map matching among others), these subgraph matching methods do not work. We propose a method for identifying the node correspondence between a subgraph and a full graph in the inexact case without node labels in two steps -(a) extract the minimal unique topology preserving subset from the subgraph and find its feasible matching in the full graph, and (b) implement a consensus-based algorithm to expand the matched node set by pairing unique paths based on boundary commutativity. Going beyond the existing subgraph matching approaches, the proposed method is shown to have realistically sub-linear computational efficiency, robustness to random measurement noise, and good statistical properties. Our method is also readily applicable to the exact matching case without loss of generality. To demonstrate the effectiveness of the proposed method, a simulation and a case study is performed on the Erdos-Renyi random graphs and the image-based affine covariant features dataset respectively.
