A connected component and transitive closure parallel algorithm using pointer jumping technique is presented in this paper, which runs on n×n wormhole routed 2D mesh in time O(log²n). A minimum spanning tree (MST) parallel algorithm running on the same model in time O(log³n) is also presented. These improve the lower time bound O(n) on n×n store-and-forward routed 2D mesh. Compared with other known algorithms running on various non-bus-connected parallel machines with distributed memory, the time complexity of the connected component and transitive closure parallel algorithm is optimal.