Ping Pong in Dangerous Graphs: Optimal Black Hole Search with Pure Tokens

Paola Flocchini (1) , David Ilcinkas (2, 3) , Nicola Santoro (4)

1 Distributed Computing Research Group [Ottawa]
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique
3 CEPAGE - Algorithmics for computationally intensive applications over wide scale distributed platforms
4 School of Computer Science [Ottawa]

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 {\em 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 $\Theta(n \log n)$ moves, where $n$ is the number of nodes, even when the links are not FIFO.

Keywords: distributed computing; graph exploration; mobile agents; autonomous robots; dangerous graphs

Domains: Distributed, Parallel, and Cluster Computing [cs.DC]; Data Structures and Algorithms [cs.DS]

Paola Flocchini, David Ilcinkas, Nicola Santoro. Ping Pong in Dangerous Graphs: Optimal Black Hole Search with Pure Tokens. DISC 2008, Sep 2008, France. pp.227-241, ⟨10.1007/978-3-540-87779-0_16⟩. ⟨hal-00341523⟩