A logical calculus of the ideas immanent in nervous activity
Neurocomputing: foundations of research
Randomized algorithms
Spreading of messages in random graphs
CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
| Hi-index | 0.00 |
We model a network in which messages spread by a simple directed graph G= (V,E) [8] and a function 茂戮驴: V茂戮驴茂戮驴 mapping each v茂戮驴 Vto a positive integer less than or equal to the indegree of v. The graph Grepresents the individuals in the network and the communication channels between them. An individual v茂戮驴 Vwill be convinced of a message when at least 茂戮驴(v) of its in-neighbors are convinced. Suppose we are to convince a message to all individuals by convincing a subset S茂戮驴 Vof individuals at the beginning and then let the message spread. We study minimum-sized sets Sneeded to convince all individuals at the end. In particular, our results include a lower bound on the size of a minimum Sand the NP-completeness of computing a minimum S. Our lower bound utilizes a technique in [9]. Finally, we analyze the special case where each individual is convinced of a message when more than half of its in-neighbors are convinced.