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

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 worst-case, 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)logn/loglogn + bD _b ) steps for arbitrary networks, if b≤k/2. In the case when b≤k/2, $bD_b=O(\sqrt{n})$ and $k = O(\sqrt{n})$, we give a refined algorithm which completes exploration in asymptotically optimal O(n/k) steps.

Research supported in part by Royal Society Grant ESEP 16244, COST Action TIST 293 (GRAAL), and a visiting fellowship from LaBRI/ENSEIRB for Colin Cooper.