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Balancing m-ary search trees with compressions on the fringe

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Abstract

We investigate the performance of random m-ary trees grown under an algorithm that perfectly balances k levels, whenever the opportunity arises in a fringe subtree. The average-case analysis shows that considerable saving in space and search time is achieved by such a fringe balancing algorithm.

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Notes

  1. The and: in the conditional statement is the abortive version, which does not check the second condition if the first is false.

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Acknowledgements

The authors sincerely thank two anonymous reviewers for their careful scrutiny and insightful remarks which significantly improved the exposition.

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Authors and Affiliations

  1. Department of Statistics, The George Washington University, Washington, DC, 20052, USA

    Shuyang Gao & Hosam Mahmoud

  2. Department of Mechanical and Electrical Engineering, Damascus University, Damascus, Syria

    Leen Hatem

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  1. Shuyang Gao
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  2. Leen Hatem
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  3. Hosam Mahmoud
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Correspondence to Hosam Mahmoud.

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Gao, S., Hatem, L. & Mahmoud, H. Balancing m-ary search trees with compressions on the fringe. Acta Informatica 61, 53–66 (2024). https://doi.org/10.1007/s00236-023-00448-2

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