# On Optimal Neighbor Discovery

## TL;DR

This paper establishes the fundamental limits on neighbor discovery latency under energy constraints, revealing that some existing protocols are already optimal and highlighting future directions for robustness improvements.

## Contribution

It provides the first tight, duty-cycle-dependent bounds on worst-case discovery latency, clarifying the optimality of current protocols and guiding future research.

## Key findings

- Several existing protocols are proven to be optimal.
- No further latency reduction is possible under current energy constraints.
- Future protocols can focus on robustness against beacon collisions.

## Abstract

Mobile devices apply neighbor discovery (ND) protocols to wirelessly initiate a first contact within the shortest possible amount of time and with minimal energy consumption. For this purpose, over the last decade, a vast number of ND protocols have been proposed, which have progressively reduced the relation between the time within which discovery is guaranteed and the energy consumption. In spite of the simplicity of the problem statement, even after more than 10 years of research on this specific topic, new solutions are still proposed even today. Despite the large number of known ND protocols, given an energy budget, what is the best achievable latency still remains unclear. This paper addresses this question and for the first time presents safe and tight, duty-cycle-dependent bounds on the worst-case discovery latency that no ND protocol can beat. Surprisingly, several existing protocols are indeed optimal, which has not been known until now. We conclude that there is no further potential to improve the relation between latency and duty-cycle, but future ND protocols can improve their robustness against beacon collisions.