Local Sequence (LS) Based Rendezvous Algorithms

Abstract

In this chapter, we present symmetric algorithms for the blind rendezvous problem between two asynchronous, non-anonymous users. In the rendezvous setting, we fix \({ Alg}\), \({ Time}\), and \({ ID}\) as follows: $$\begin{aligned} RS = \end{aligned}$$ (9.1) where \(Port \in \{Port-S, Port-AS\}\), which implies that we design efficient algorithms that have good performance for both symmetric and asymmetric port situations. In designing Global Sequence (GS) based rendezvous algorithms for two anonymous users, many time slots are wasted since the user has to access a random available port if the pre-defined port in the sequence is not available. Since the users have no distinguishable identifiers, they have to obey the global sequence, which is verified to be an efficient method. However, if the users have identifiers (IDs), they are non-anonymous and they can decide on different hopping sequences based on its local information. GS based rendezvous algorithms construct a sequence of fixed length for all users and it is inefficient when the number of available ports accounts for only a small fraction of all external ports. Thus, we propose Local Sequence (LS) based rendezvous algorithms which construct different sequences on the basis of the local information for different users. In this chapter, we introduce LS based rendezvous algorithms where different users hop among their available ports according to different sequences, which are different from GS based algorithms in terms of intuition. By adopting the LS based rendezvous algorithms, the users may achieve rendezvous in a shorter time comparing with the GS based algorithms when the available ports are only a small fraction of all external ports. In Sect. 9.1, we give the motivation for constructing LS and present a simple example to illustrate. We first present the Ring Walk algorithm in Sect. 9.2, which constructs different sequences on the basis of the user’s ID. Then, we present the Alternate Hop-and-Wait (AHW) algorithm in Sect. 9.3, which combines the hop and wait strategies. Two efficient LS based rendezvous algorithms are provided in Sects. 9.4 and 9.5 respectively, where the first one guarantees rendezvous in O(N) and \(O(N^2)\) time slots for two port-symmetric and port-asymmetric users respectively, and the latter guarantees rendezvous in \(O(|C_i|)\) and \(O((\max \{|C_i|,|C_j|\})^2)\) time slots for two port-symmetric and port-asymmetric users respectively, where \(C_i, C_j\) represent the available port sets of two users. Finally, we summarize the chapter in Sect. 9.6.