Searching for a dangerous host: randomized vs. deterministic

A Black Hole is an harmful host in a network that destroys incoming agents without leaving any trace of such event. The problem of locating the black hole in a network through a team of agent coordinated by a common protocol is usually referred in literature as the Black Hole Search problem (or BHS for brevity) and it is a consolidated research topic in the area of distributed algorithms [3]. The aim of this paper is to extend the results for BHS by considering more general (and hence harder) classes of dangerous host. In particular we introduce rB-hole as a probabilistic generalization of the Black Hole, in which the destruction of an incoming agent is a purely random event happening with some fixed probability (like flipping a biased coin). The main result we present is that if we tolerate an arbitrarily small error probability in the result then the rB-hole Search problem, or rBHS, is not harder than the usual BHS. We establish this result in two different communication model, specifically both in presence or absence of whiteboards non-located at the homebase. The core of our methods is a general reduction tool for transforming algorithms for the black hole into algorithms for the rB-hole.