Abstract
In this paper, a heuristic method for the optimal placement of monitors in communication networks is proposed. In order to be able to make informed decisions, a first step towards securing a communication network is deploying an adequate sensor infrastructure. However, appropriate monitoring should take into account the priority of the communication links as well as the location of monitors. The goal is to cover the whole network with the minimum investment and impact on performance, i.e., the optimal amount and positions of monitors in the network. In order to be able to counteract dynamic changes in those networks, e.g., link failures, attacks, or entering and leaving nodes, this work focuses on swiftly obtaining results having an acceptable quality. To achieve this goal, an effective hybrid search heuristic is introduced, combining the computational efficiency of a greedy local search method with the robustness of evolution-based heuristics. It is shown that this approach works well on synthetic benchmark instances and real-world network models, having up to millions of nodes, by comparing the performance of a common evolutionary algorithm (EA) to its hybrid search counterparts. It is observed that the hybrid search heuristics produce good solutions on the instances under study in a reasonable amount of time. Regarding the fitness of the solutions found, the hybrid approach outperforms the common EA in all the experiments. Moreover, on all problem instances, the hybrid EA finds the best solutions significantly earlier in the search process, which is key when monitoring a communication infrastructure which is subject to change.
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In the seminal work by Karp (1972), a decision version of the vertex-cover problem is proved \(\mathcal {NP}\)-complete. A property of \(\mathcal {NP}\)-complete problems is that computing exact solutions is not efficient, i.e. all algorithms known take exponential time in the size of the instance. Finding exact solutions to arbitrary instances of a given \(\mathcal {NP}\)-complete problem becomes impractical as their size increases (van Leeuwen 1990).
The complement of a vertex cover in a graph is an independent set, thus a minimum vertex cover can be straightforwardly recovered from a maximum independent set.
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Acknowledgements
This work was supported in the framework of Hessen ModellProjekte, financed with funds of the European Union (European Regional Development Fund-ERDF) and the State of Hessen in the context of the research project “Reactive network Optimization by Using SDN-Technology” (ROBUST) (HA Project No. 473/15-15), and the Spanish Ministry of Economy and Competitiveness (National Program for Research, Development and Innovation) and with funds of the European Union (European Regional Development Fund-ERDF), project DArDOS TIN2015-65845-C3-3-R and project FAME (RTI2018-093608-B-C33). Responsible for the content are the authors.
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Mueller-Bady, R., Kappes, M., Medina-Bulo, I. et al. An evolutionary hybrid search heuristic for monitor placement in communication networks. J Heuristics 25, 861–899 (2019). https://doi.org/10.1007/s10732-019-09414-z
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DOI: https://doi.org/10.1007/s10732-019-09414-z