Searching for a black hole in arbitrary networks: optimal mobile agents protocols

Abstract

Consider a networked environment, supporting mobile agents, where there is a black hole: a harmful host that disposes of visiting agents upon their arrival, leaving no observable trace of such a destruction. The black hole search problem is the one of assembling a team of asynchronous mobile agents, executing the same protocol and communicating by means of whiteboards, to successfully identify the location of the black hole; we are concerned with solutions that are generic (i.e., topology-independent). We establish tight bounds on the size of the team (i.e., the number of agents), and the cost (i.e., the number of moves) of a size-optimal solution protocol. These bounds depend on the a priori knowledge the agents have about the network, and on the consistency of the local labellings. In particular, we prove that: with topological ignorance ∆ + 1 agents are needed and suffice, and the cost is Θ(n 2 ), where ∆ is the maximal degree of a node and n is the number of nodes in the network; with topological ignorance but in presence of sense of direction only two agents suffice and the cost is Θ(n 2 ); and with complete topological knowledge only two agents suffice and the cost is Θ(n log n). All the upper-bound proofs are constructive.

Scattered Black Hole Search in an Oriented Ring using Tokens

“…The computational issues related to the presence of a harmful agent have been explored in the context of intruder capture and network decontamination; in the case of harmful host, the focus has been on the black hole (BH), a node that disposes of any incoming agent without leaving any observable trace of this destruction [2,3,5,6,7,8,9,10,13]. In this paper, we continue the investigation of the black hole search problem.…”

“…The computability and complexity of BHS depend on a variety of factors, first and foremost on whether the system is asynchronous [5,6,7,8,9] or synchronous [2,4,3,13]. Indeed the nature of the problem changes drastically and dramatically.…”

“…In particular, in [10] it was shown that a team of two or more colocated agents can solve BHS with O(n log n) moves and two (2) tokens per agent in a ring network. Notice that the ring is the sparsest bi-connected graph (bi-connectivity is required for BHS in asynchronous systems [8]), and for which the number of moves for black hole search with whiteboards is the worst.…”

Searching for Black-Hole Faults in a Network Using Multiple Agents

“…The black hole search was studied in [3,4,5] under the scenario of totally asynchronous networks, that is, without assuming any bound on the ratio of the times of two different edge traversals. The authors considered the case of two agents and one black hole.…”

Finding Short Right-Hand-on-the-Wall Walks in Graphs

“…However, Sense of Direction is more general and can be used in ways our construction cannot (e.g. avoiding entering a node -see [15]. )…”