A Note to Non-adaptive Broadcasting

• Published in: Parallel processing letters Vol. 34; no. 1
• Main Authors: Gholami, Saber, Harutyunyan, Hovhannes A.
• Format: Journal Article
• Language: English
• Published: Singapore World Scientific Publishing Company 01.03.2024; World Scientific Publishing Co. Pte., Ltd
• Subjects: Broadcasting; Graphs; Upper bounds; Broadcasting; universal lists; non-adaptive
• ISSN: 0129-6264; 1793-642X
• DOI: 10.1142/S0129626423400170

Broadcasting is a fundamental problem in the information dissemination area. In classical broadcasting, a message must be sent from one network member to all other members as rapidly as feasible. Although it has been demonstrated that this problem is NP-Hard for arbitrary graphs, it has several applications in various fields. As a result, the universal lists model, replicating real-world restrictions like the memory limits of nodes in large networks, is introduced as a branch of this problem in the literature. In the universal lists model, each node is equipped with a fixed list and has to follow the list regardless of the originator. In this study, we focus on the non-adaptive branch of universal lists broadcasting. In this regard, we establish the optimal broadcast time of k -ary trees and binomial trees under the non-adaptive model and provide an upper bound for complete bipartite graphs. We also improved a general upper bound for trees under the same model and showed that our upper bound cannot be improved in general.