176 research outputs found
Efficient, Optimal -Leader Selection for Coherent, One-Dimensional Formations
We study the problem of optimal leader selection in consensus networks with
noisy relative information. The objective is to identify the set of leaders
that minimizes the formation's deviation from the desired trajectory
established by the leaders. An optimal leader set can be found by an exhaustive
search over all possible leader sets; however, this approach is not scalable to
large networks. In recent years, several works have proposed approximation
algorithms to the -leader selection problem, yet the question of whether
there exists an efficient, non-combinatorial method to identify the optimal
leader set remains open. This work takes a first step towards answering this
question. We show that, in one-dimensional weighted graphs, namely path graphs
and ring graphs, the -leader selection problem can be solved in polynomial
time (in both and the network size ). We give an solution for
optimal -leader selection in path graphs and an solution for
optimal -leader selection in ring graphs.Comment: 7 pages, 5 figures, submitted to ECC1
- …