2021/08/28 by Liyan Chen, Samuel Cheng, Chen, Liyan +5
Computer Science · #Caching and Content Delivery #Cooperative Communication and Network Coding #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Electrical engineering #Internet Traffic Analysis and Secure E-voting #Signal Processing (eess.SP) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2109.00339
openalex publication_date 2021/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The shift-enabled property of an underlying graph is essential in designing distributed filters. This article discusses when a random graph is shift-enabled. In particular, popular graph models ER, WS, BA random graph are used, weighted and unweighted, as well as signed graphs. Our results show that the considered unweighted connected random graphs are shift-enabled with high probability when the number of edges is moderately high. However, very dense graphs, as well as fully connected graphs, are not shift-enabled. Interestingly, this behaviour is not observed for weighted connected graphs, which are always shift-enabled unless the number of edges in the graph is very low.