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

Abstract

Abstract. We consider a fixed communication network where (software) agents can move freely from node to node along the edges. A black hole is a faulty or malicious node in the network such that if an agent enters this node, then it immediately "dies." We are interested in designing an efficient communication algorithm for the agents to identify all black holes. We assume that we have k agents starting from the same node s and knowing the topology of the whole network. The agents move through the network in synchronous steps and can communicate only when they meet in a node. At the end of the exploration of the network, at least one agent must survive and must know the exact locations of the black holes. If the network has n nodes and b black holes, then any exploration algorithm needs Ω(n/k + D b ) steps in the worstcase, where D b is the worst case diameter of the network with at most b nodes deleted. We give a general algorithm which completes exploration in O((n/k) log n/ log log n+bD b ) steps for arbitrary networks, if b ≤ k/2. In the case when, we give a refined algorithm which completes exploration in asymptotically optimal O(n/k) steps.

Time Optimal Algorithms for Black Hole Search in Rings

“…We also show that any asynchronous black hole search algorithm for rings requires T average (n, k) = 3 2 n time regardless of the number k > 1 of agents, and then prove that, with 2(n − 1) agents, the optimal average case complexity 3 2 n − O(1) can be achieved without increasing the worst case. Finally, observing that all considered protocols achieve (worst and average) Θ(n) time using O(n) agents, we prove that it is possible to locate a black hole in asymptotically optimal (worst and average) Θ(n) time with just k = 2 agents.…”

“…Algorithm OptAvgTime solves the black hole location problem. in average ideal time complexity 3 2 n + O(1) and worst case ideal time complexity 2(n − 2). Both complexities are optimal.…”

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.…”

Rendezvous of Mobile Agents in Unknown Graphs with Faulty Links

“…The objective here is minimizing the number of agents that fall into the black hole and the time taken by the surviving agents to locate the black hole [20]. The general case of multiple black holes has been considered only by Cooper et al [8]. All these problems assume that the team of agents start from the same node, i.e.…”