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Annual Symposium on Combinatorial Pattern Matching

CPM 2013: Combinatorial Pattern Matching pp 235–246Cite as

A Succinct Grammar Compression

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7922)

Abstract

We solve an open problem related to an optimal encoding of a straight line program (SLP), a canonical form of grammar compression deriving a single string deterministically. We show that an information-theoretic lower bound for representing an SLP with n symbols requires at least 2n + logn! + o(n) bits. We then present a succinct representation of an SLP; this representation is asymptotically equivalent to the lower bound. The space is at most 2nlogρ(1 + o(1)) bits for \(\rho \leq 2\sqrt{n}\), while supporting random access to any production rule of an SLP in O(loglogn) time. In addition, we present a novel dynamic data structure associating a digram with a unique symbol. Such a data structure is called a naming function and has been implemented using a hash table that has a space-time tradeoff. Thus, the memory space is mainly occupied by the hash table during the development of production rules. Alternatively, we build a dynamic data structure for the naming function by leveraging the idea behind the wavelet tree. The space is strictly bounded by 2nlogn(1 + o(1)) bits, while supporting O(logn) query and update time.

Keywords

  • Directed Acyclic Graph
  • Production Rule
  • Query Time
  • Naming Function
  • Entropy Bound

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This study was supported by KAKENHI(23680016,20589824) and JST PRESTO program.

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Author information

Authors and Affiliations

  1. JST, ERATO Minato Project, Japan

    Yasuo Tabei

  2. Kyushu Institute of Technology, Japan

    Yoshimasa Takabatake & Hiroshi Sakamoto

  3. JST, PRESTO, Japan

    Hiroshi Sakamoto

Authors
  1. Yasuo Tabei
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  2. Yoshimasa Takabatake
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  3. Hiroshi Sakamoto
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Editor information

Editors and Affiliations

  1. Fakultät für Informatik, Institut für Theoretische Informatik, Karlsruhe Institut für Technology, Am Fasanengarten 5, 76131, Karlsruhe, Germany

    Johannes Fischer

  2. Karlsruhe Institute of Technology, Germany

    Peter Sanders

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Tabei, Y., Takabatake, Y., Sakamoto, H. (2013). A Succinct Grammar Compression. In: Fischer, J., Sanders, P. (eds) Combinatorial Pattern Matching. CPM 2013. Lecture Notes in Computer Science, vol 7922. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38905-4_23

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  • DOI: https://doi.org/10.1007/978-3-642-38905-4_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38904-7

  • Online ISBN: 978-3-642-38905-4

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