  We study the French-DeGroot opinion dynamics in a social network with two
polarizing parties. We consider a network in which the leaders of one party are
given, and we pose the problem of selecting the leader set of the opposing
party so as to shift the average opinion to a desired value. When each party
has only one leader, we express the average opinion in terms of the transition
matrix and the stationary distribution of random walks in the network. The
analysis shows balance of influence between the two leader nodes. We show that
the problem of selecting at most $k$ absolute leaders to shift the average
opinion is $\mathbf{NP}$-hard. Then, we reduce the problem to a problem of
submodular maximization with a submodular knapsack constraint and an additional
cardinality constraint and propose a greedy algorithm with upper bound search
to approximate the optimum solution. We also conduct experiments in random
networks and real-world networks to show the effectiveness of the algorithm.
