Asynchronous Gathering in a Dangerous Ring

Consider a set of k identical asynchronous mobile agents located in an anonymous ring n nodes. The classical Gather (or Rendezvous) problem requires all to meet at the same node, not priori decided, within finite amount time. This has been studied assuming that network is safe for agents. In this paper, we consider presence stationary process node disables any incoming agent without leaving trace. Such dangerous known literature as black hole, and determination its location extensively investigated. hole makes it deterministically unfeasible gather. So, research concern determine how many can gather under what conditions. paper establish complete characterization conditions which be solved. particular, maximum number guaranteed depending on whether or unknown (at least one must known). These results are tight: each case, gathering with more unfeasible. All our possibility proofs constructive: provide algorithms allow predefined distance specified analysis time costs these show they optimal. Our algorithm case also solution problem. Interestingly, bounded complexity Θ(n); significant improvement over existing O(nlogn) complexity.