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Quantum Query Complexity of Some Graph Problems

Authors:

Christoph Dürr,

Mark Heiligman,

Peter HOyer,

Mehdi MhallaAuthors Info & Claims

SIAM Journal on Computing, Volume 35, Issue 6

Pages 1310 - 1328

https://doi.org/10.1137/050644719

Published: 01 June 2006 Publication History

Abstract

Quantum algorithms for graph problems are considered, both in the adjacency matrix model and in an adjacency list-like array model. We give almost tight lower and upper bounds for the bounded error quantum query complexity of Connectivity, Strong Connectivity, Minimum Spanning Tree, and Single Source Shortest Paths. For example, we show that the query complexity of Minimum Spanning Tree is in $\Theta(n^{3/2})$ in the matrix model and in $\Theta(\sqrt{nm})$ in the array model, while the complexity of Connectivity is also in $\Theta(n^{3/2})$ in the matrix model but in $\Theta(n)$ in the array model. The upper bounds utilize search procedures for finding minima of functions under various conditions.

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Ren JSui YCheng XFeng YZhao J(2024)Dynamic Transitive Closure-based Static Analysis through the Lens of Quantum SearchACM Transactions on Software Engineering and Methodology10.1145/364438933:5(1-29)Online publication date: 4-Jun-2024
https://dl.acm.org/doi/10.1145/3644389
Gao MJi ZLi TWang QOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Logarithmic-regret quantum learning algorithms for zero-sum gamesProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3667481(31177-31203)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.5555/3666122.3667481
Drias HDrias YHouacine NBendimerad LZouache DKhennak I(2023)Quantum OPTICS and deep self-learning on swarm intelligence algorithms for Covid-19 emergency transportationSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-022-06946-827:18(13181-13200)Online publication date: 1-Sep-2023
https://dl.acm.org/doi/10.1007/s00500-022-06946-8
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Index Terms

Quantum Query Complexity of Some Graph Problems
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
      2. Paths and connectivity problems
2. Theory of computation
  1. Randomness, geometry and discrete structures

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Published In

SIAM Journal on Computing Volume 35, Issue 6

2006

243 pages

ISSN:0097-5397

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Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 June 2006

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Ren JSui YCheng XFeng YZhao J(2024)Dynamic Transitive Closure-based Static Analysis through the Lens of Quantum SearchACM Transactions on Software Engineering and Methodology10.1145/364438933:5(1-29)Online publication date: 4-Jun-2024
https://dl.acm.org/doi/10.1145/3644389
Gao MJi ZLi TWang QOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Logarithmic-regret quantum learning algorithms for zero-sum gamesProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3667481(31177-31203)Online publication date: 10-Dec-2023
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Drias HDrias YHouacine NBendimerad LZouache DKhennak I(2023)Quantum OPTICS and deep self-learning on swarm intelligence algorithms for Covid-19 emergency transportationSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-022-06946-827:18(13181-13200)Online publication date: 1-Sep-2023
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Cooper C(2022)Exploring Potential Applications of Quantum Computing in Transportation ModellingIEEE Transactions on Intelligent Transportation Systems10.1109/TITS.2021.313216123:9(14712-14720)Online publication date: 1-Sep-2022
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Darbari PGibney DThankachan S(2022)Quantum Time Complexity and Algorithms for Pattern Matching on Labeled GraphsString Processing and Information Retrieval10.1007/978-3-031-20643-6_22(303-314)Online publication date: 8-Nov-2022
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Lee TSantha MZhang SMarx D(2021)Quantum algorithms for graph problems with cut queriesProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458123(939-958)Online publication date: 10-Jan-2021
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Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity

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