Memory Efficient Very-Large Colored Subgraph Detection

Algorithms for the exact detection of a subgraph S within a larger graph G are currently limited to a small number of vertices in S. In colored graphs, the problem is simpler, given the constraint induced by the color match. We here propose VELCRO: (Very Efficient Large Colored subgRaph detectiOn) to detect very large colored subgraphs. VELCRO is based on efficient memory management to avoid multiplying the constraint memory cost for each vertex combination tested, smart traversal of vertices in S, and a constraint on the degree of the next vertex. In short, VELCRO orders the vertices in S and opens a Depth First Search (DFS) in G to search pathways consistent with S. At each stage, VELCRO efficiently tests the constraints on unmatched vertices in S. The vertex order is optimized to prevent an exponential growth in the number of candidate trajectories by maximizing future constraints. VELCRO stops a path when any vertex in S is constrained to have no possible match in G. We show the efficacy of VELCRO on simulated dense G(n,p)G(n,p), real-world colored graphs, and real-world graphs with random coloring. VELCRO was tested on S of up to 5×105 vertices and on G up to millions of vertices and solves the queries within seconds to minutes. No current exact subgraph matching algorithm can search such large colored subgraphs.