多通道會合問題是許多物聯網應用中，鄰近發現的一個基本問題。現有文獻主要著重於改善最壞情況的表現，而平均情況的表現通常不如隨機演算法。由於物聯網設備（用戶）彼此相近，它們的可用通道集雖然可能不同，但非常相似。我們使用數據挖掘中的局部敏感哈希（LSH）技術，提出了一種通道跳躍算法，利用這兩個可用通道集之間的相似性，增加會合概率。
我們考慮了兩種設定，在同步的設定下，我們的算法的平均會合時間（ETTR）與
一個被稱為 Jaccard 指數的知名相似度指數成反比。Jaccard 指數是兩個集合之間相似性的度量，定義為它們的交集大小除以它們的聯集大小。對於非同步設定，我們使用降維技術加快會合過程，讓平均會合時間進一步降低。
此外，我們結合了 LSH 方法和 MACH 序列，將 LSH 的序列嵌入到 MACH 序列
以確保最大會合時間 (MTTR) 的上限。最後，我們限制了隨機時鐘漂移，提出了帶有LSH 技術的算法，以確保會合時間並分析 MTTR 的上限。我們的數值結果顯示，當Jaccard 指數高時，我們的算法在 ETTR 方面可以優於隨機算法。這表示我們所提出的算法能夠有效利用設備可用通道集之間的相似性，增加會合概率。

The multichannel rendezvous problem is a fundamental problem for neighbor discovery in many IoT applications. The existing works in the literature focus mostly on improving the worst-case performance, and the average-case performance is often not as good as that of the random algorithm. As IoT devices (users) are close to each other, their available channel sets, though they might be different, are similar. Using the locality-sensitive hashing (LSH) technique in data mining, we propose channel hopping algorithms that exploit the similarity between the two available channel sets to increase the rendezvous probability.
For the synchronous setting, our algorithms have the expected time-to-rendezvous (ETTR) inversely proportional to a well-known similarity measure called the Jaccard index. For the asynchronous setting, we use dimensionality reduction to speed up the rendezvous process. Furthermore, we embed the sequence generated by LSH to an Asynchronous Channel Hopping sequence with Maximum rendezvous diversity (MACH)
sequence to ensure the upper bound of MTTR. Finally, we limit the random clock drift and propose an algorithm with LSH technique to ensure the time of rendezvous and analyze the upper bound of MTTR.
Our numerical results show that our algorithms can outperform the random algorithm in terms of ETTR when the Jaccard index is high.

Contents 1
List of Figures 4
1 Introduction 5
2 The multichannel rendezvous problem 9
2.1 Problem Formulation 9
2.2 Related work about synchronous setting 10
2.3 Related work about asynchronous setting 11
3 The synchronous setting 13
3.1 Locality-sensitive hashing 13
3.2 Channel hopping algorithms 15
4 The asynchronous setting 22
4.1 Direct extension 22
4.2 Dimensionality reduction 27
4.3 LSH with a bounded MTTR 29
4.4 Bounded clock drift 31
5 Simulations 39
5.1 Numerical results in the synchronous setting 39
5.2 Numerical results in the asynchronous setting 42
5.3 Numerical results for LSH with a bounded MTTR 45
5.4 Numerical results for the setting with a bounded clock drift 47
6 Conclusion 50

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