We consider the following multi–level opinion spreading model in networks. Initially, each node gets a weight from the set {0, ..., k − 1}; where the weight of a node tells how much the actor, represented by the node, is convinced of the new idea (or product). Then, the process proceeds in rounds; during each round each node updates its weight depending on the weights of its neighbors. We are interested in the initial assignments of weights leading each node to get the value k − 1 –e.g. unanimous maximum level acceptance– within a given number of rounds. We determine lower bounds on the sum of the initial weights of the nodes under the irreversible simple majority rules, where a node increases its weight if and only if the majority of its neighbors have a weight that is higher than its own one. Moreover, we provide constructive tight upper bounds for some class of regular topologies: rings, tori, and cliques.
Minimum Weight Dynamo and Fast Opinion Spreading
CORDASCO, Gennaro;
2012
Abstract
We consider the following multi–level opinion spreading model in networks. Initially, each node gets a weight from the set {0, ..., k − 1}; where the weight of a node tells how much the actor, represented by the node, is convinced of the new idea (or product). Then, the process proceeds in rounds; during each round each node updates its weight depending on the weights of its neighbors. We are interested in the initial assignments of weights leading each node to get the value k − 1 –e.g. unanimous maximum level acceptance– within a given number of rounds. We determine lower bounds on the sum of the initial weights of the nodes under the irreversible simple majority rules, where a node increases its weight if and only if the majority of its neighbors have a weight that is higher than its own one. Moreover, we provide constructive tight upper bounds for some class of regular topologies: rings, tori, and cliques.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
