On the Multichannel Rendezvous Problem without Global Channel Enumeration

The multichannel rendezvous problem, which requires two users to find each other by hopping among their available channels over time, is a crucial step for neighborhood discovery in many IoT applications. In the literature, it is commonly assumed that a global channel enumeration exists (according to a certain international standard), allowing channels to be indexed from 1 to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex>. In this paper, we address the multichannel rendezvous problem without relying on global channel enumeration. Instead, we simply assume that each channel is associated with a frequency that has an L-bit identifier (ID). Inspired by consistent hashing used in data centers and peer-to-peer networks, we propose low-complexity, locality-sensitive hashing (LC-LSH) channel-hopping algorithms. For the synchronous setting, our LC- LSH algorithm exhibits an expected time-to-rendezvous (ETTR) that is inversely proportional to the Jaccard index of the available channel sets of the two users. We demonstrate that our algorithm can also be extended to the asynchronous setting by employing a dimensionality reduction technique.