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Compressed Data Structures for Dynamic Sequences

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Algorithms - ESA 2015

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9294))

Abstract

We consider the problem of storing a dynamic string S over an alphabet Σ = { 1,…,σ } in compressed form. Our representation supports insertions and deletions of symbols and answers three fundamental queries: returns the i-th symbol in S, counts how many times a symbol a occurs among the first i positions in S, and finds the position where a symbol a occurs for the i-th time. We present the first fully-dynamic data structure for arbitrarily large alphabets that achieves optimal query times for all three operations and supports updates with worst-case time guarantees. Ours is also the first fully-dynamic data structure that needs only nH k  + o(nlogσ) bits, where H k is the k-th order entropy and n is the string length. Moreover our representation supports extraction of a substring S[i..i + ℓ] in optimal O(logn/loglogn + ℓ/log σ n) time.

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Authors and Affiliations

  1. David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada

    J. Ian Munro & Yakov Nekrich

Authors
  1. J. Ian Munro
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  2. Yakov Nekrich
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Editors and Affiliations

  1. University of Technology, Eindhoven, The Netherlands

    Nikhil Bansal

  2. Sapienza University of Rome, Rome, Italy

    Irene Finocchi

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Munro, J.I., Nekrich, Y. (2015). Compressed Data Structures for Dynamic Sequences. In: Bansal, N., Finocchi, I. (eds) Algorithms - ESA 2015. Lecture Notes in Computer Science(), vol 9294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48350-3_74

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  • DOI: https://doi.org/10.1007/978-3-662-48350-3_74

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-48349-7

  • Online ISBN: 978-3-662-48350-3

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