Deterministic Protocols in the SINR Model without Knowledge of Coordinates

Much work has been developed for studying the classical broadcasting problem in the SINR (Signal-to-Interference-plus-Noise-Ratio) model for wireless device transmission. The setting typically studied is when all radio nodes transmit a signal of the same strength. This work studies the challenging problem of devising a distributed algorithm for multi-broadcasting, assuming a subset of nodes are initially awake, for the SINR model when each device only has access to knowledge about the total number of nodes in the network \(n\), the range from which each node's label is taken \(\lbrace 1,\dots,N \rbrace\), and the label of the device itself. Specifically, we assume no knowledge of the physical coordinates of devices and also no knowledge of the neighborhood of each node. We present a deterministic protocol for this problem in \(O(n \lg N \lg n)\) rounds. There is no known polynomial time deterministic algorithm in literature for this setting, and it remains the principle open problem in this domain. A lower bound of \(\Omega(n \lg N)\) rounds is known for deterministic broadcasting without local knowledge. In addition to the above result, we present algorithms to achieve multi-broadcast in \(O(n \lg N)\) rounds and create a backbone in \(O(n \lg N)\) rounds, assuming that all nodes are initially awake. For a given backbone, messages can be exchanged between every pair of connected nodes in the backbone in \(O(\lg N)\) rounds and between any node and its designated contact node in the backbone in \(O(\Delta \lg N)\) rounds.