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Space Efficient Data Structures for Nearest Larger Neighbor

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Combinatorial Algorithms (IWOCA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8986))

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  • International Workshop on Combinatorial Algorithms

Abstract

Given a sequence of n elements from a totally ordered set, and a position in the sequence, the nearest larger neighbor (NLN) query returns the position of the element which is closest to the query position, and is larger than the element at the query position. The problem of finding all nearest larger neighbors has attracted interest due to its applications for parenthesis matching and in computational geometry [1–3]. We consider a data structure version of this problem, which is to preprocess a given sequence of elements to construct a data structure that can answer NLN queries efficiently. We consider time-space tradeoffs for the problem in both the encoding (where the input is not accessible after the data structure has been created) and indexing model, and consider cases when the input is in a one or two dimensional array. We also consider the version when only the nearest larger right neighbor (NLRN) is sought (in one dimension). We initiate the study of this problem in two dimensions, and describe upper and lower bounds in the encoding and indexing models, distinguishing the two cases when all the elements are distinct or non-distinct.

Seungbum Jo and Rao Satti—Research partly supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant number 2012-0008241).

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Author information

Authors and Affiliations

  1. Chennai Mathematical Institute, Chennai, India

    Varunkumar Jayapaul

  2. Seoul National University, Seoul, South Korea

    Seungbum Jo & Srinivasa Rao Satti

  3. The Institute of Mathematical Sciences, Chennai, India

    Venkatesh Raman

Authors
  1. Varunkumar Jayapaul
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  2. Seungbum Jo
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  3. Venkatesh Raman
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  4. Srinivasa Rao Satti
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Corresponding author

Correspondence to Srinivasa Rao Satti .

Editor information

Editors and Affiliations

  1. Faculty of Mathematics and Physics, Charles University, Praha, Czech Republic

    Kratochvíl Jan

  2. University of Newcastle, Newcastle, New South Wales, Australia

    Mirka Miller

  3. University of Minnesota, Duluth Department of Mathematics, Duluth, Minnesota, USA

    Dalibor Froncek

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Jayapaul, V., Jo, S., Raman, V., Satti, S.R. (2015). Space Efficient Data Structures for Nearest Larger Neighbor. In: Jan, K., Miller, M., Froncek, D. (eds) Combinatorial Algorithms. IWOCA 2014. Lecture Notes in Computer Science(), vol 8986. Springer, Cham. https://doi.org/10.1007/978-3-319-19315-1_16

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  • DOI: https://doi.org/10.1007/978-3-319-19315-1_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19314-4

  • Online ISBN: 978-3-319-19315-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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