# Deterministic Protocols in the SINR Model without Knowledge of Coordinates

## TL;DR

This paper introduces a deterministic multi-broadcast protocol in the SINR wireless model without coordinate knowledge, achieving near-optimal round complexity and enabling efficient backbone construction.

## Contribution

It presents the first polynomial-time deterministic algorithms for multi-broadcast and backbone creation in the SINR model without local knowledge.

## Key findings

- Deterministic multi-broadcast protocol runs in O(n log N log n) rounds.
- Algorithms for multi-broadcast and backbone creation in O(n log N) rounds.
- Efficient message exchange within the backbone in O(log N) rounds.

## Abstract

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.