IVE: Accelerating Enumeration-Based Subgraph Matching via Exploring Isolated Vertices

The performance of the enumeration-based sub-graph matching, which searches all isomorphic subgraphs in the data graph, is crucial to various applications. The upper bound of the complexity for the enumeration-based method is exponential to the number of query graph vertices, denoted as
$n$
. We propose a novel subgraph matching algorithm called the Isolated Vertices Exploration (IVE). The IVE leverages isolated vertices during the reordering and enumeration phases, thereby significantly accelerating the subgraph matching process. During the enumeration, the isolated vertices can be matched by using a quick bipartite graph matching algorithm. Consequently, the complexity of matching the remaining non-isolated vertices is exponential to the number of non-isolated vertices, denoted as
$n^{\prime}$
. For the reordering, we designed the Maximum Deleted Edges (MDE) to minimize
$n^{\prime}$
. MDE iteratively selects the query vertex with the maximum edges. According to the experimental results,
$n^{\prime}$
is less than
$0.8n$
for 99.8% of arbitrary graphs. Moreover, IVE outperforms the state-of-the-art algorithms in various scenarios with different sizes, sparsities and fields, achieving a performance speedup of up to 80.3x.