Research on a Graph Reachability Algorithm Based on Block Optimization

The traditional Floyd Warshall algorithm can be used to compute the transitive closure of a graph with
$O \boldsymbol{(\mathrm{n}^{\wedge}3)}$
time complexity. In this paper, a new directed graph reachability calculation algorithm based on topological sorting and block optimization is proposed. The performance of the new algorithm is verified by simulation experiments under different conditions. The experimental results show that the new algorithm is more effective than the traditional algorithm when calculating the reachability of directed graphs with different sparsity.