Abstract
In order to formulate mathematical conjectures likely to be true, a number of base cases must be determined. However, many combinatorial problems are NP-hard and the computational complexity makes this research approach difficult using a standard brute force approach on a typical computer. One sample problem explored is that of finding a minimum identifying code. To work around the computational issues, a variety of methods are explored and consist of a parallel computing approach using MATLAB, an adiabatic quantum optimization approach using a D-Wave quantum annealing processor, and lastly using satisfiability modulo theory (SMT) and corresponding SMT solvers. Each of these methods requires the problem to be formulated in a unique manner. In this paper, we address the challenges of computing solutions to this NP-hard problem with respect to each of these methods.
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Acknowledgments
The work using the D-Wave quantum annealing machine was performed jointly by AFRL/RI and Lockheed Martin under Air Force Cooperative Research and Development Agreement 14-RI-CRADA-02. S. Adachi was supported by Internal Research and Development funding from Lockheed Martin. S. Adachi would also like to thank Todd Belote and Dr. Andy Dunn of Lockheed Martin for their assistance, respectively, with the SAT-to-Ising mapping in Sect. 2.2 and with the generation of models for the scaling analysis of larger cases in Sect. 2.5. LOCKHEED MARTIN and LOCKHEED are registered trademarks in the U.S. Patent and Trademark Office owned by Lockheed Martin Corporation.
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Approved for public release; distribution unlimited: 88ABW-2015-2163, DIS201511002.
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Horan, V., Adachi, S. & Bak, S. A comparison of approaches for finding minimum identifying codes on graphs. Quantum Inf Process 15, 1827–1848 (2016). https://doi.org/10.1007/s11128-016-1240-0
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DOI: https://doi.org/10.1007/s11128-016-1240-0