TL;DR
This paper analyzes three signal routing schemes on weighted trees, establishing precise conditions on transceiver and edge weights that determine the feasibility of long-distance transmission from the root.
Contribution
It introduces and characterizes three routing schemes on weighted trees, providing sharp probabilistic conditions for successful long-range signal transmission.
Findings
Derived sharp conditions for root transmission feasibility
Identified critical weight distribution thresholds
Compared different routing schemes' effectiveness
Abstract
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Graph Theory Research · Cooperative Communication and Network Coding · Interconnection Networks and Systems