Efficient Subgraph Similarity Search on Large Probabilistic Graph Databases

Many studies have been conducted on seeking the efficient solution for subgraph similarity search over certain (deterministic) graphs due to its wide application in many fields, including bioinformatics, social network analysis, and Resource Description Framework (RDF) data management. All these works assume that the underlying data are certain. However, in reality, graphs are often noisy and uncertain due to various factors, such as errors in data extraction, inconsistencies in data integration, and privacy preserving purposes. Therefore, in this paper, we study subgraph similarity search on large probabilistic graph databases. Different from previous works assuming that edges in an uncertain graph are independent of each other, we study the uncertain graphs where edges’ occurrences are correlated. We formally prove that subgraph similarity search over probabilistic graphs is #P-complete, thus, we employ a filter-and-verify framework to speed up the search. In the filtering phase,we develop tight lower and upper bounds of subgraph similarity probability based on a probabilistic matrix index, PMI. PMI is composed of discriminative subgraph features associated with tight lower and upper bounds of subgraph isomorphism probability. Based on PMI, we can sort out a large number of probabilistic graphs and maximize the pruning capability. During the verification phase, we develop an efficient sampling algorithm to validate the remaining candidates. The efficiency of our proposed solutions has been verified through extensive experiments.

💡 Research Summary

The paper tackles the problem of subgraph similarity search over large probabilistic graph databases where edge occurrences are not independent but correlated. Recognizing that many real‑world networks (e.g., biological interaction networks, social graphs, RDF knowledge bases) contain noise, extraction errors, and privacy‑induced uncertainty, the authors move beyond the traditional assumption of independent edges. They formally define the Probability of Subgraph Similarity (PSP) as the probability that a query graph Q can be transformed into a subgraph of a data graph G within a given edit‑distance threshold τ. By reducing PSP computation to counting satisfying assignments in a probabilistic model, they prove that exact PSP evaluation is #P‑complete, establishing the inherent computational hardness of the task.

To achieve practical performance, the authors propose a filter‑and‑verify framework.
Filtering Phase:

• They construct a Probabilistic Matrix Index (PMI) that stores a set of highly discriminative subgraph features (patterns). For each feature f and each data graph G, PMI records a lower bound L(G,f) and an upper bound U(G,f) on the probability that f appears in G. The lower bound assumes edge independence and can be computed quickly as a product of individual edge probabilities; the upper bound incorporates edge correlations via inclusion‑exclusion adjustments, yielding a tighter envelope.
• The query graph Q is decomposed into the same feature set. By aggregating the feature‑level bounds, the system derives a global interval (