Abstract
Motivated by applications in diagnosing failures in complex infrastructure networks, we consider the configuration sequence completion problem (CSC) for networked systems. The goal of the CSC problem is to choose values for unknown entries in a specified sequence of configurations of a system so that the resulting sequence represents a valid trajectory of the system. This problem generalizes some known decision problems for dynamical systems. We present efficient algorithms for some versions of the CSC problem and computational intractability results for other versions.
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- 1.
Configurations with no predecessors are called Garden of Eden configurations.
- 2.
See [7] for the definition of treewidth.
- 3.
The definition of r-symmetric functions appears in Sect. 2.
- 4.
Haimes and Jiang [16] propose a dynamical model similar to the one discussed here but do not discuss the computational aspects which is crucial.
- 5.
The value of the k-threshold function is 1 iff at least k of the inputs are 1 [10].
- 6.
The instantaneous description of a 1-tape machine consists of the state of the TM, contents of the tape and the head position.
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Acknowledgments
We thank Professors Arun Phadke and late Jim Thorp (Virginia Tech) for discussions related to problems studied in this paper. We thank the referees for providing helpful comments. This work has been partially supported by DARPA Cooperative Agreement D17AC00003 (NGS2), DTRA CNIMS (Contract HDTRA1-11-D-0016-0001), NSF DIBBS Grant ACI-1443054, NSF BIG DATA Grant IIS-1633028 and NSF EAGER Grant CMMI-1745207.
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Marathe, M.V., Ravi, S.S., Rosenkrantz, D.J., Stearns, R.E. (2019). Computational Aspects of Fault Location and Resilience Problems for Interdependent Infrastructure Networks. In: Aiello, L., Cherifi, C., Cherifi, H., Lambiotte, R., Lió, P., Rocha, L. (eds) Complex Networks and Their Applications VII. COMPLEX NETWORKS 2018. Studies in Computational Intelligence, vol 812. Springer, Cham. https://doi.org/10.1007/978-3-030-05411-3_70
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