2014/07/11 by Maria Deijfen, Deijfen, Maria, Nina Gantert +1 · 2 citations
Computer Science · Mathematics · #Advanced Graph Theory Research #Cooperative Communication and Network Coding #FOS: Mathematics #Interconnection Networks and Systems #Probability (math.PR) #math.PR
paper · pdf · doi:10.48550/arxiv.1407.3190
arxiv created 2014/07/11 · openalex publication_date 2014/07/11 · arxiv updated 2014/07/14 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
We consider three different schemes for signal routing on a tree. The vertices of the tree represent transceivers that can transmit and receive signals, and are equipped with i.i.d. weights representing the strength of the transceivers. The edges of the tree are also equipped with i.i.d. weights, representing the costs for passing the edges. For each one of our schemes, we derive sharp conditions on the distributions of the vertex weights and the edge weights that determine when the root can transmit a signal over arbitrarily large distances.