Ping Pong in Dangerous Graphs: Optimal Black Hole Search with Pebbles

Authors:
Paola Flocchini;David Ilcinkas;Nicola Santoro
Affiliations:
University of Ottawa, SITE, K1N 6N5, Ottawa, ON, Canada;CNRS & Universitéé de Bordeaux, LaBRI, Bordeaux, France;Carleton University, SCS, K1S 5B6, Ottawa, Ontario, Canada
Venue:
Algorithmica
Year:
2012

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Abstract

We prove that, for the black hole search problem in networks of arbitrary but known topology, the pebble model of agent interaction 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(nlog n) moves, where n is the number of nodes, even when the links are not FIFO. These results are obtained with a novel algorithmic technique, ping-pong, for agents using pebbles.