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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 labelings. In particular, we prove that: with topological ignorance Δ+1 agents are needed and suffice, and the cost is Θ(n 2), where Δ 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.

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Author information

Correspondence to Stefan Dobrev.

Additional information

A preliminary version of this paper appeared in the Proceedings of the 21st ACM Symposium on Principles of Distributed Computing [21].

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Dobrev, S., Flocchini, P., Prencipe, G. et al. Searching for a black hole in arbitrary networks: optimal mobile agents protocols. Distrib. Comput. 19, 1–99999 (2006). https://doi.org/10.1007/s00446-006-0154-y

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Keywords

  • Mobile agents
  • Malicious host
  • Distributed search
  • Black hole
  • Topological knowledge