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Quantum Combine and Conquer and Its Applications to Sublinear Quantum Convex Hull and Maxima Set Construction

Authors Shion Fukuzawa , Michael T. Goodrich , Sandy Irani

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Subject Classification

ACM Subject Classification
  • Theory of computation
Keywords
  • quantum computing
  • computational geometry
  • divide and conquer
  • convex hulls
  • maxima sets

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Abstract

We introduce a quantum algorithm design paradigm called combine and conquer, which is a quantum version of the "marriage-before-conquest" technique of Kirkpatrick and Seidel. In a quantum combine-and-conquer algorithm, one performs the essential computation of the combine step of a quantum divide-and-conquer algorithm prior to the conquer step while avoiding recursion. This model is better suited for the quantum setting, due to its non-recursive nature. We show the utility of this approach by providing quantum algorithms for 2D maxima set and convex hull problems for sorted point sets running in Õ(√{nh}) time, w.h.p., where h is the size of the output.

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Shion Fukuzawa, Michael T. Goodrich, and Sandy Irani. Quantum Combine and Conquer and Its Applications to Sublinear Quantum Convex Hull and Maxima Set Construction. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 51:1-51:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SoCG.2025.51

Author Details

Shion Fukuzawa
  • University of California, Irvine, CA, USA
Michael T. Goodrich
  • University of California, Irvine, CA, USA
Sandy Irani
  • University of California, Irvine, CA, USA

Funding

This work was supported in part by NSF Grant 2212129.

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