Follower distribution algorithms for leader-follower networks

In this paper, three follower distribution algorithms, (1) shortest-path follower distribution, (2) even follower distribution, and (3) hybrid follower distribution algorithms, are described for arbitrary leader-follower networks with pre-selected leaders. The shortest-path follower distribution algorithm is designed to minimize the path length that connects a leader to its followers while distributing followers among each leader as evenly as possible. It is shown that employing the shortest-path follower distribution algorithm with sorted greedy-based matching provides follower distributions with the smallest variance. The even follower distribution algorithm is designed to prioritize even distribution of followers among leaders over minimization of the length of path between each leader and its followers. The hybrid follower distribution algorithm is designed to prioritize goals according to a user-defined percentage, where increment of the user-defined percentage corresponds to increment in the priority of the minimization of the length of path that connects a leader to its followers over even distribution of followers. The resulting follower distributions that correspond to different user-defined percentages are illustrated on an arbitrary leader-follower network.