Multiple Agents RendezVous in a Ring in Spite of a Black Hole

Abstract

The Rendezvous of anonymous mobile agents in a anonymous network is an intensively studied problem; it calls for k anonymous, mobile agents to gather in the same site. We study this problem when in the network there is a black hole: a stationary process located at a node that destroys any incoming agent without leaving any trace. The presence of the black hole makes it clearly impossible for all agents to rendezvous. So, the research concern is to determine how many agents can gather and under what conditions.In this paper we consider k anonymous, asynchronous mobile agents in an anonymous ring of size n with a black hole; the agents are aware of the existence, but not of the location of such a danger. We study the rendezvous problem in this setting and establish a complete characterization of the conditions under which the problem can be solved. In particular, we determine the maximum number of agents that can be guaranteed to gather in the same location depending on whether k or n is unknown (at least one must be known for any nontrivial rendezvous). These results are tight: in each case, rendezvous with one more agent is impossible.All our possibility proofs are constructive: we provide mobile agents protocols that allow the agents to rendezvous or near-gather under the specified conditions. The analysis of the time costs of these protocols show that they are optimal.Our rendezvous protocol for the case when k is unknown is also a solution for the black hole location problem. Interestingly, its bounded time complexity is Θ(n); this is a significant improvement over the O(n log n) bounded time complexity of the existing protocols for the same case.

Deterministic Symmetric Rendezvous in Arbitrary Graphs: Overcoming Anonymity, Failures and Uncertainty

“…Given a graph with multiple faulty nodes, we can merge them all into one dangerous node x, called the black hole. The question of whether rendezvous can be solved in a graph containing a black hole was first studied in [18] where an algorithm was provided for ring graphs containing a single black hole. We study the problem for arbitrary graphs with both faulty nodes and faulty edges, where the agents do not have prior knowledge of the graph topology or the possible location of faults.…”

“…We can ensure that no more than one agent dies while traversing the same link, using the cautious walk technique as in [18]. At each node, all the incident edges are considered to be unexplored in the beginning.…”

Rendezvous of Mobile Agents in Directed Graphs

“…[4,10,16,17,19]). The problem has been studied for specific topologies such as rings [11], tori [17], trees [15] as well as in the most general case of an unlabeled terrain [14]. The idea of solving rendezvous by marking the starting locations with tokens was first proposed by Baston and Gal [5].…”

“…leader election is another such problem) that are central to study of computability in distributed systems. The importance of the problem is evident from the large volume of literature [10,11,[14][15][16][17]19] dedicated to solving the problem under various conditions and restrictions.…”

“…Exploration of unknown and unlabeled graphs (or digraphs) is difficult unless the agents are allowed to mark the nodes. As in several previous papers on the topic [3,4,9,11,13], we allow the agents to mark nodes of the digraphs by writing on whiteboards available at each node.…”