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A Query-Efficient Quantum Algorithm for Maximum Matching on General Graphs

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Algorithms and Data Structures (WADS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12808))

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Abstract

We design quantum algorithms for maximum matching. Working in the query model, in both adjacency matrix and adjacency list settings, we improve on the best known algorithms for general graphs, matching previously obtained results for bipartite graphs. In particular, for a graph with n vertices and m edges, our algorithm makes \(O(n^{7/4})\) queries in the matrix model and \(O(n^{3/4}(m+n)^{1/2})\) queries in the list model. Our approach combines Gabow’s classical maximum matching algorithm [Gabow, Fundamenta Informaticae, ’17] with the guessing tree method of Beigi and Taghavi [Beigi and Taghavi, Quantum, ’20].

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Notes

  1. 1.

    One can easily extend to the case that G is a subgraph of a multigraph; we consider complete graphs only for simplicity.

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Authors and Affiliations

  1. Department of Computer Science, Middlebury College, Middlebury, USA

    Shelby Kimmel

  2. Department of Computer Science and Engineering, NYU Tandon School of Engineering, New York City, USA

    R. Teal Witter

Authors
  1. Shelby Kimmel
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  2. R. Teal Witter
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Correspondence to R. Teal Witter .

Editor information

Editors and Affiliations

  1. University of Waterloo, Waterloo, ON, Canada

    Anna Lubiw

  2. University of Alberta, Edmonton, AB, Canada

    Mohammad Salavatipour

  3. Dalhousie University, Halifax, Canada

    Meng He

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Kimmel, S., Witter, R.T. (2021). A Query-Efficient Quantum Algorithm for Maximum Matching on General Graphs. In: Lubiw, A., Salavatipour, M., He, M. (eds) Algorithms and Data Structures. WADS 2021. Lecture Notes in Computer Science(), vol 12808. Springer, Cham. https://doi.org/10.1007/978-3-030-83508-8_39

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  • DOI: https://doi.org/10.1007/978-3-030-83508-8_39

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-030-83508-8

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