A network of agents must maintain connectivity while pursuing individual objectives. Adding an edge (a communication link) between two agents improves connectivity but costs energy. Removing an edge reduces overhead but risks fragmentation. The topology control problem: which edges to add and which to remove, dynamically, as the network evolves.
The paper proposes a leader-based distributed mechanism. A dynamically elected leader evaluates the network's current topology and broadcasts edge addition or deletion commands. The leader selection rotates based on a local criterion — the agent with the best connectivity metric becomes the temporary leader. The mechanism is distributed (no central controller) but coordinated (the leader provides coherence).
The key property: the mechanism provably maintains connectivity at all times while allowing the topology to adapt. Edge deletions are safe — the mechanism never removes an edge whose deletion would disconnect the network. Edge additions are strategic — they target the most beneficial connections, measured by algebraic connectivity (the second-smallest Laplacian eigenvalue).
The dynamic leader rotation prevents single points of failure. If the current leader fails, a new leader is elected automatically. The leader's role is coordination, not computation — the topological decisions are based on local connectivity metrics that any agent can compute. The distributed mechanism achieves the same connectivity guarantees as a centralized controller without requiring global knowledge at any single node.
Topology as a control variable, not a fixed parameter. The network doesn't just operate on a graph — it actively shapes the graph to maintain performance. The controller's output is the network itself.