Consistent Channel Hopping Algorithms for the Multichannel Rendezvous Problem with Heterogeneous Available Channel Sets

2025-06-23

AI Summary

This paper addresses the multi-channel rendezvous problem (MRP) in wireless networks under heterogeneous available channel sets. Method: We propose a channel-hopping algorithmic framework with guaranteed consistency. Its core innovation lies in proving that all consistent channel-selection functions are equivalent—under channel relabeling—to selecting the minimum-index channel, enabling a natural permutation-sequence representation. We theoretically derive that the expected time-to-rendezvous equals the reciprocal of the Jaccard similarity of the involved channel sets, and show this bound is tight. Furthermore, we design a low-complexity modular-arithmetic algorithm integrating single-cycle permutations and locality-sensitive hashing (LSH) principles, augmented with a multi-user coordination mechanism. Contribution/Results: We establish tight bounds on both worst-case and expected rendezvous times. Simulations confirm that the proposed algorithm achieves high rendezvous probability, low latency, and excellent scalability under both synchronous and asynchronous settings, approaching the theoretical LSH upper bound.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Search and Optimization: Algorithm Configuration
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

We propose a theoretical framework for consistent channel hopping algorithms to address the multichannel rendezvous problem (MRP) in wireless networks with heterogeneous available channel sets. A channel selection function is called consistent if the selected channel remains unchanged when the available channel set shrinks, provided the selected channel is still available. We show that all consistent channel selection functions are equivalent to the function that always selects the smallest-index channel under appropriate channel relabeling. This leads to a natural representation of a consistent channel hopping algorithm as a sequence of permutations. For the two-user MRP, we characterize rendezvous time slots using a fictitious user and derive tight bounds on the maximum time-to-rendezvous (MTTR) and expected time-to-rendezvous (ETTR). Notably, the ETTR is shown to be the inverse of the Jaccard index when permutations are randomly selected. We also prove that consistent channel hopping algorithms maximize the rendezvous probability. To reduce implementation complexity, we propose the modulo algorithm, which uses modular arithmetic with one-cycle permutations and achieves performance comparable to locality-sensitive hashing (LSH)-based algorithms. The framework is extended to multiple users, with novel strategies such as stick-together, spread-out, and a hybrid method that accelerates rendezvous in both synchronous and asynchronous settings. Simulation results confirm the effectiveness and scalability of the proposed algorithms.

Problem

• Develop consistent channel hopping for multichannel rendezvous in wireless networks
• Characterize rendezvous time slots and derive tight bounds on MTTR and ETTR
• Extend framework to multiple users with novel rendezvous strategies

Innovation

• Consistent channel hopping with smallest-index selection
• Modulo algorithm using modular arithmetic
• Hybrid method for multi-user rendezvous