Consistent Subgraph Matching over Large Graphs

Subgraph matching over graphs has been extensively studied, due to its wide applications in knowledge bases, social networks, and among others. To catch the inconsistency and errors that commonly exist in these graphs, this paper studies consistent subgraph matching (CSM), i.e., finding the common matches in every consistent graph repair w.r.t a set of conditional graph dependencies (CGDs). We concentrate on subset, superset and symmetric difference graph repairs. We study fundamental problems for CGDs and CSM. We show that the satisfiability, implication, and validation problems of CGDs are coNP-complete, coNP-complete and NP-complete, respectively. We also show that the CSM problem (under any kind of repair) is NP-complete. We provide (parallel) algorithms to solve CSM, and guarantee to reduce running time when given more processors. Using reallife and synthetic graphs, we empirically verify the efficiency and effectiveness of our algorithms.