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Network Decontamination

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Distributed Computing by Mobile Entities

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11340))

Abstract

The Network Decontamination problem consists of coordinating a team of mobile agents in order to clean a contaminated network. The problem is actually equivalent to tracking and capturing an invisible and arbitrarily fast fugitive. This problem has natural applications in network security in computer science or in robotics for search or pursuit-evasion missions. Many different objectives have been studied: the main one being the minimization of the number of mobile agents necessary to clean a contaminated network.

Many environments (continuous or discrete) have also been considered. In this Chapter, we focus on networks modeled by graphs. In this context, the optimization problem that consists of minimizing the number of agents has a deep graph-theoretical interpretation. Network decontamination and, more precisely, graph searching models, provide nice algorithmic interpretations of fundamental concepts in the Graph Minors theory by Robertson and Seymour.

For all these reasons, graph searching variants have been widely studied since their introduction by Breish (1967) and mathematical formalizations by Parsons (1978) and Petrov (1982). This chapter consists of an overview of the algorithmic results on graph decontamination and graph searching.

This work has been partially supported by ANR program “Investments for the Future” under reference ANR-11-LABX-0031-01, the Inria Associated Team AlDyNet.

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Notes

  1. 1.

    We should emphasize that there is another different topic of graph theory, related to Depth/Breadth First Search, called Graph Searching, a.k.a. Graph Traversals (e.g. [CDH+16]).

  2. 2.

    Unless stated otherwise, all graphs considered in this chapter are simple, undirected, and connected.

  3. 3.

    Given a graph \(G=(V,E)\) and \(v \in V\), N(v) denotes the set of neighbors of v, i.e., \(N(v)=\{u \in V \mid uv \in E\}\).

  4. 4.

    A minor of a graph G is any subgraph of any graph obtained from G by contracting some edges.

  5. 5.

    Due to the huge number of works on treewidth, we have decided not to detail them (nor the definition of treewidth) and refer the reader to [Bod98, Die12, CFK+15].

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    Nicolas Nisse

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Nisse, N. (2019). Network Decontamination. In: Flocchini, P., Prencipe, G., Santoro, N. (eds) Distributed Computing by Mobile Entities. Lecture Notes in Computer Science(), vol 11340. Springer, Cham. https://doi.org/10.1007/978-3-030-11072-7_19

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