Searching for a dangerous host: randomized vs. deterministic

TL;DR

This paper investigates the problem of locating probabilistic dangerous hosts, called rB-holes, in networks, showing that with minimal error tolerance, the search complexity is comparable to deterministic black holes across different communication models.

Contribution

It introduces the rB-hole as a probabilistic generalization of black holes and demonstrates that search algorithms can be adapted with minimal error, unifying deterministic and probabilistic cases.

Findings

RBS is not harder than BHS with small error tolerance

The reduction method transforms BHS algorithms into RBS algorithms

Results hold in multiple communication models

Abstract

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. 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 RBS, 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.