Tight Bounds for Black Hole Search with Scattered Agents in Synchronous Rings

TL;DR

This paper establishes tight bounds on the minimal number of identical, memory-limited agents and tokens needed to detect a black hole in synchronous ring networks, advancing understanding in resource-efficient black hole search.

Contribution

It provides the first deterministic algorithms with matching bounds for black hole search using scattered agents with constant memory and tokens in ring networks.

Findings

Matching lower and upper bounds for agents and tokens required

Deterministic algorithms for black hole detection in rings

Applicable to both oriented and unoriented rings

Abstract

We study the problem of locating a particularly dangerous node, the so-called black hole in a synchronous anonymous ring network with mobile agents. A black hole is a harmful stationary process residing in a node of the network and destroying destroys all mobile agents visiting that node without leaving any trace. We consider the more challenging scenario when the agents are identical and initially scattered within the network. Moreover, we solve the problem with agents that have constant-sized memory and carry a constant number of identical tokens, which can be placed at nodes of the network. In contrast, the only known solutions for the case of scattered agents searching for a black hole, use stronger models where the agents have non-constant memory, can write messages in whiteboards located at nodes or are allowed to mark both the edges and nodes of the network with tokens. This paper solves the problem for ring networks containing a single black hole. We are interested in the minimum resources (number of agents and tokens) necessary for locating all links incident to the black hole. We present deterministic algorithms for ring topologies and provide matching lower and upper bounds for the number of agents and the number of tokens required for deterministic solutions to the black hole search problem, in oriented or unoriented rings, using movable or unmovable tokens.