最小权发电机与快速意见传播
Minimum Weight Dynamo and Fast Opinion Spreading
摘要：
我们考虑了以下网络上的多层次意见传播模型。最初，每个节点从集合[0. k-1]，其中这样的权重代表个人对新想法或产品的信念。然后，通过进行轮，每个节点根据其邻居的权重更新其权重。我们感兴趣的是权重的初始分配，导致每个节点在给定的轮数内获得值k-1 -例如一致的最大水平接受。我们确定下界的不可逆简单多数规则下的节点的初始权重的总和，其中一个节点增加其权重，当且仅当大多数的邻居有一个权重高于自己的。此外，我们提供了建设性的紧上界的一些定期拓扑类：环，环面，和集团。
英文摘要：
We consider the following multi--level opinion spreading model on networks. Initially, each node gets a weight from the set [0..k-1], where such a weight stands for the individuals conviction of a new idea or product. Then, by proceeding to rounds, each node updates its weight according to 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.
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