Random Walks, Interacting Particles, Dynamic Networks: Randomness Can Be Helpful

Self-stabilizing repeated balls-into-bins

“…The process terminates when the token has visited all nodes of the system. Randomized protocols for this problem [8] are efficient approaches when, for instance, the network is prone to faults/changes and/or when there is no global labeling of the nodes, e.g., the network is anonymous.…”

“…A simple randomized protocol is the one based on random walks [5,8,9]: starting from any node, the token performs a random walk over the network until all nodes are visited, w.h.p. The first round in which all nodes have been visited by the token is called the cover time of the random walk [8,10].…”

“…The first round in which all nodes have been visited by the token is called the cover time of the random walk [8,10]. The expected cover time for general graphs is O(|V | · |E|) (see, e.g., [11]).…”

“…balls), each of them starting from a node (i.e. bins) of the complete graph of size n. This is a randomized protocol for the multi-token traversal problem where tokens represent different resources/tasks that must be assigned to all nodes in mutual exclusion [8]. In this scenario, a critical complexity measure is the (global) cover time, i.e., the time required by any token to visit all nodes.…”

“…This line of research is also motivated by several recent applications of parallel random walks in the (uniform) gossip model [8,13,14,40]. As mentioned in the introduction, previous analysis of this process provides a bound O √ t on the maximum load after t rounds on regular graphs [12].…”