Improving state-of-the-art vertex sorting algorithms to compute the maximum common induced subgraph

The Maximum Common Induced Subgraph problem is a longstanding challenge in graph theory and combinatorial optimization, recognized for being NP-complete and its applications across chemistry, network analysis, and pattern recognition. State-of-the-art methods, such as the McSplit algorithm and its successors, employ a recursive branch-and-bound procedure to navigate the vast solution space. The efficiency of this search is critically dependent on the initial vertex sorting heuristic, which not only guides the algorithm toward a good solution but also structures the search tree for the computationally intensive proof of optimality. The original algorithm relies on a simple node degree heuristic, which is often suboptimal. This paper systematically investigates the influence of alternative vertex-ordering heuristics on McSplitDAL, a state-of-the-art variant of McSplit. We integrate five node-ranking heuristics (namely, PageRank, Betweenness Centrality, Closeness Centrality, Local Clustering Coefficient, and a modified Katz Centrality) into the McSplitDAL framework. We analyze their effect on search-space exploration, pruning efficiency, convergence behavior, and execution speed. We also investigate how they shape the algorithmic search and affect the solver’s ability to approach or prove optimality under constrained computational budgets. Experimental results across heterogeneous datasets reveal that specific heuristics, such as PageRank and Katz Centrality, consistently promote more effective pruning and higher-quality intermediate solutions, offering valuable insights into the relationship between graph topology-derived measures and branch-and-bound performance.