Ping pong in dangerous graphs: Optimal black hole search with pure tokens

Abstract

We prove that, for the black hole search problem, the pure token model is computationally as powerful as the whiteboard model; furthermore the complexity is exactly the same. More precisely, we prove that a team of two asynchronous agents, each endowed with a single identical pebble (that can be placed only on nodes, and with no more than one pebble per node) can locate the black hole in an arbitrary network of known topology; this can be done with Θ(n log n) moves, where n is the number of nodes, even when the links are not FIFO. © 2008 Springer-Verlag Berlin Heidelberg.