Abstract
A recent breakthrough by Ambainis, Balodis, Iraids, Kokainis, Prūsis and Vihrovs (SODA’19) showed how to construct faster quantum algorithms for the Traveling Salesman Problem and a few other NP-hard problems by combining in a novel way quantum search with classical dynamic programming. In this paper, we show how to apply this approach to the minimum Steiner tree problem, a well-known NP-hard problem, and construct the first quantum algorithm that solves this problem faster than the best known classical algorithms. More precisely, the complexity of our quantum algorithm is, where n denotes the number of vertices in the graph and k denotes the number of terminals. In comparison, the best known classical algorithm has complexity.
Cite
CITATION STYLE
Miyamoto, M., Iwamura, M., Kise, K., & Gall, F. L. (2020). Quantum Speedup for the Minimum Steiner Tree Problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 12273 LNCS, pp. 234–245). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-58150-3_19
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