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Quantum Algorithms for the Most Frequently String Search, Intersection of Two String Sequences and Sorting of Strings Problems

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Theory and Practice of Natural Computing (TPNC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11934))

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Abstract

We study algorithms for solving three problems on strings. The first one is the Most Frequently String Search Problem. The problem is the following. Assume that we have a sequence of n strings of length k. The problem is finding the string that occurs in the sequence most often. We propose a quantum algorithm that has a query complexity \(\tilde{O}(n \sqrt{k})\). This algorithm shows speed-up comparing with the deterministic algorithm that requires \(\varOmega (nk)\) queries.

The second one is searching intersection of two sequences of strings. All strings have the same length k. The size of the first set is n and the size of the second set is m. We propose a quantum algorithm that has a query complexity \(\tilde{O}((n+m) \sqrt{k})\). This algorithm shows speed-up comparing with the deterministic algorithm that requires \(\varOmega ((n+m)k)\) queries.

The third problem is sorting of n strings of length k. On the one hand, it is known that quantum algorithms cannot sort objects asymptotically faster than classical ones. On the other hand, we focus on sorting strings that are not arbitrary objects. We propose a quantum algorithm that has a query complexity \(O(n (\log n)^2 \sqrt{k})\). This algorithm shows speed-up comparing with the deterministic algorithm (radix sort) that requires \(\varOmega ((n+d)k)\) queries, where d is a size of the alphabet.

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Acknowledgments

This work was supported by Russian Science Foundation Grant 19-71-00149. We thank Aliya Khadieva, Farid Ablayev and Kazan Federal University quantum group for useful discussions.

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Authors and Affiliations

  1. Smart Quantum Technologies Ltd., Kazan, Russia

    Kamil Khadiev

  2. Kazan Federal University, Kazan, Russia

    Kamil Khadiev & Artem Ilikaev

Authors
  1. Kamil Khadiev
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  2. Artem Ilikaev
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Correspondence to Kamil Khadiev .

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Editors and Affiliations

  1. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  2. Royal Military College of Canada, Kingston, ON, Canada

    Geoffrey Pond

  3. University of Extremadura, Cáceres, Spain

    Miguel A. Vega-Rodríguez

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Khadiev, K., Ilikaev, A. (2019). Quantum Algorithms for the Most Frequently String Search, Intersection of Two String Sequences and Sorting of Strings Problems. In: Martín-Vide, C., Pond, G., Vega-Rodríguez, M. (eds) Theory and Practice of Natural Computing. TPNC 2019. Lecture Notes in Computer Science(), vol 11934. Springer, Cham. https://doi.org/10.1007/978-3-030-34500-6_17

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  • DOI: https://doi.org/10.1007/978-3-030-34500-6_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-34499-3

  • Online ISBN: 978-3-030-34500-6

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