Spreading Messages

Abstract. We model a network in which messages spread by a simple directed graph G = (V, E) [1] and a function : V N mapping each v V to a positive integer less than or equal to the indegree of v. The graph G represents the individuals in the network and the communication channels between them. An individual v V will be convinced of a message when at least (v) of its in-neighbors are convinced. Suppose we are to convince a message to all individuals by convincing a subset S V of individuals at the beginning and then let the message spread. We study the minimum possible size of S needed to convince all individuals at the end. In particular, our results include a lower bound on the size of a minimum S and the NP-completeness of computing a minimum S. Our lower bound utilizes a technique in [2]. Finally, we analyze the special case where each individual is convinced of a message when more than half of its in-neighbors are convinced.

• Type: Conference
• Year: 2008
• Where: COCOON
• Authors: Ching-Lueh Chang, Yuh-Dauh Lyuu
• Keywords: COCOON 2008, Combinatorics, Communication Channels, Positive Integer, Simple Directed Graph