49,216 research outputs found
Joint Centrality Distinguishes Optimal Leaders in Noisy Networks
We study the performance of a network of agents tasked with tracking an
external unknown signal in the presence of stochastic disturbances and under
the condition that only a limited subset of agents, known as leaders, can
measure the signal directly. We investigate the optimal leader selection
problem for a prescribed maximum number of leaders, where the optimal leader
set minimizes total system error defined as steady-state variance about the
external signal. In contrast to previously established greedy algorithms for
optimal leader selection, our results rely on an expression of total system
error in terms of properties of the underlying network graph. We demonstrate
that the performance of any given set of leaders depends on their influence as
determined by a new graph measure of centrality of a set. We define the of a set of nodes in a network graph such that a leader set with
maximal joint centrality is an optimal leader set. In the case of a single
leader, we prove that the optimal leader is the node with maximal information
centrality. In the case of multiple leaders, we show that the nodes in the
optimal leader set balance high information centrality with a coverage of the
graph. For special cases of graphs, we solve explicitly for optimal leader
sets. We illustrate with examples.Comment: Conditionally accepted to IEEE TCN
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
Adaptive Network Dynamics and Evolution of Leadership in Collective Migration
The evolution of leadership in migratory populations depends not only on
costs and benefits of leadership investments but also on the opportunities for
individuals to rely on cues from others through social interactions. We derive
an analytically tractable adaptive dynamic network model of collective
migration with fast timescale migration dynamics and slow timescale adaptive
dynamics of individual leadership investment and social interaction. For large
populations, our analysis of bifurcations with respect to investment cost
explains the observed hysteretic effect associated with recovery of migration
in fragmented environments. Further, we show a minimum connectivity threshold
above which there is evolutionary branching into leader and follower
populations. For small populations, we show how the topology of the underlying
social interaction network influences the emergence and location of leaders in
the adaptive system. Our model and analysis can describe other adaptive network
dynamics involving collective tracking or collective learning of a noisy,
unknown signal, and likewise can inform the design of robotic networks where
agents use decentralized strategies that balance direct environmental
measurements with agent interactions.Comment: Submitted to Physica D: Nonlinear Phenomen
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