The fastest known classical algorithm deciding the k-colorability of n-vertex graph requires running time Ω (2n) for k≥ 5. In this work, we present an exponential-space quantum algorithm computing the chromatic number with running time O(1. 9140n) using quantum random access memory (QRAM). Our approach is based on Ambainis et al.’s quantum dynamic programming with applications of Grover’s search to branching algorithms. We also present a polynomial-space quantum algorithm not using QRAM for the graph 20-coloring problem with running time O(1. 9575n). For the polynomial-space quantum algorithm, we essentially show (4 - ϵ)n-time classical algorithms that can be improved quadratically by Grover’s search.
CITATION STYLE
Shimizu, K., & Mori, R. (2020). Exponential-Time Quantum Algorithms for Graph Coloring Problems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 12118 LNCS, pp. 387–398). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-61792-9_31
Mendeley helps you to discover research relevant for your work.