Asynchronous Deterministic Rendezvous on the Line

We study the rendezvous problem in the asynchronous setting in the graph of infinite line following the model introduced in [13]. We formulate general lemmas about deterministic rendezvous algorithms in this setting which characterize the algorithms in which the agents have the shortest routes. We also improve rendezvous algorithms in the infinite line which formulated in [13]. Two agents have distinct labels Lmin, Lmax and |Lmin| ≤ |Lmax|. When the initial distance D between the agents is known, our algorithm has cost D|Lmin| which is an improvement in the constant. If the initial distance is unknown we give an algorithm of cost O(D log D +D logD|Lmax|+ D|Lmin| + |Lmax||Lmin | log |Lmin|) which is an asymptotic improvement.