Abstract
This paper introduces six new failure-independent multi-path computation problems in complex networks such as smart grid communication network, each of which comes with unique failure interdependency assumptions. Despite the difference of the formulation of the problems, we show that each of the problems can be reduced to another within polynomial time, and therefore they are equivalent in terms of hardness. Then, we show that they are not only \(\mathcal {NP}\)-hard, but also cannot be approximated within a certain bound unless \(\mathcal {P}=\mathcal {NP}\). Besides, we show that their decision problem versions to determine if there exist two failure independent paths between two given end nodes are still \(\mathcal {NP}\)-complete. As a result, this paper opens a new series of research problems with daunting complexity based on important real world applications.
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Yang, Z., Kim, D., Wang, W. (2017). On Interdependent Failure Resilient Multi-path Routing in Smart Grid Communication Network. In: Gao, X., Du, H., Han, M. (eds) Combinatorial Optimization and Applications. COCOA 2017. Lecture Notes in Computer Science(), vol 10628. Springer, Cham. https://doi.org/10.1007/978-3-319-71147-8_6
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DOI: https://doi.org/10.1007/978-3-319-71147-8_6
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