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Quantum Optimization
A Grover search-based algorithm for the list coloring problem
arXiv
Authors: Sayan Mukherjee
Year
2021
Paper ID
62222
Status
Preprint
Abstract Read
~2 min
Abstract Words
99
Citations
N/A
Abstract
Graph coloring is a computationally difficult problem, and currently the best known classical algorithm for k-coloring of graphs on n vertices has runtimes Ω\(2n\) for kge 5. The list coloring problem asks the following more general question: given a list of available colors for each vertex in a graph, does it admit a proper coloring? We propose a quantum algorithm based on Grover search to quadratically speed up exhaustive search. Our algorithm loses in complexity to classical ones in specific restricted cases, but improves exhaustive search for cases where the lists and graphs considered are arbitrary in nature.
Why This Paper Matters
- This paper contributes to the Quantum Optimization research area in the Quantum Articles archive.
- It adds a 2021 reference point for readers tracking recent quantum research.
- Graph coloring is a computationally difficult problem, and currently the best known classical algorithm for k-coloring of graphs on n vertices has runtimes Ω(2^n) for kge 5.
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