Algorithms that tackle the problem of minimizing average/maximum hitting time (BMAH/BMMH) between different social network groups, given fixed shortcut edges. The contributions include(1) Proofs that BMAH problem is supermodular. (2) A 1+eps approximation algorithm using the greedy bicriteria method, which improved upon previous studies. (3) Speed up the greedy algorithm by sampling bounded-length absorbing random walks with high probability. (4) A 2+eps approximation factor for the greedy bicriteria algorithm with fast estimation. (5) Stablished a tight upper bound of BMMH using BMAH, which enabled us to derive an approximation algorithm for BMMH based on the results obtained for BMAH. (6) Stablished a connection between BMMH and the asymmetric k-median problem, which led to an approximation guarantee.