Optimal Mobile Agent Protocols for Searching a Black Hole in Arbitrary Networks

Consider a networked environment, supporting mobile agents, where there is a black hole: a harmful host that disposes of visiting agents upon their arrival, leaving no observable trace of such a destruction. The black hole search problem is the one of assembling a team of asynchronous mobile agents, executing the same protocol and communicating by means of whiteboards, to successfully identify the location of the black hole; we are concerned with solutions that are generic (i.e., topology-independent). We establish tight bounds on the size of the team (i.e., the number of agents), and the cost (i.e., the number of moves) of a size-optimal solution protocol. These bounds depend on the a priori knowledge the agents have about the network, and on the consistency of the local labellings. In particular, we prove that: with topological ignorance $\Delta+1$ agents are needed and suffice, and the cost is $\Theta(n^2)$, where $\Delta$ is the maximal degree of a node and $n$ is the number of nodes in the network; with topological ignorance but in presence of sense of direction only $two$ agents suffice and the cost is $\Theta(n^2)$; and with complete topological knowledge only $two$ agents suffice and the cost is $\Theta(n \log n)$. All the upper-bound proofs are constructive