Uncertainty-aware Efficient Subgraph Isomorphism using Graph Topology

TL;DR

This paper introduces an uncertainty-aware, efficient subgraph isomorphism method that handles inexact matching with noise and missing data, demonstrating robustness and sub-linear computational complexity in practical applications.

Contribution

The paper presents a novel two-step approach for inexact subgraph matching that is robust to noise and missing data, with improved efficiency and applicability to real-world problems.

Findings

Effective inexact matching on noisy graphs

Achieves sub-linear computational efficiency

Robust performance demonstrated on real datasets

Abstract

Subgraph isomorphism, also known as subgraph matching, is typically regarded as an NP-complete problem. This complexity is further compounded in practical applications where edge weights are real-valued and may be affected by measurement noise and potential missing data. Such graph matching routinely arises in applications such as image matching and map matching. Most subgraph matching methods fail to perform node-to-node matching under presence of such corruptions. 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. To demonstrate the effectiveness of the proposed method, a simulation is performed on the Erdos-Renyi random graphs and two case studies are performed on the image-based affine covariant features dataset and KITTI stereo dataset respectively. 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.