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Compressing Dictionary Matching Index via Sparsification Technique

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Abstract

Given a set \(\mathcal{D}\) of patterns of total length n, the dictionary matching problem is to index \(\mathcal{D}\) such that for any query text T, we can locate the occurrences of any pattern within T efficiently. This problem can be solved in optimal O(|T|+occ) time by the classical AC automaton (Aho and Corasick in Commun. ACM 18(6):333–340, 1975), where occ denotes the number of occurrences. The space requirement is O(n) words which is still far from optimal. In this paper, we show that in many cases, sparsification technique can be applied to improve the space requirements of the indexes for the dictionary matching and its related problems. First, we give a compressed index for dictionary matching, and show that such an index can be generalized to handle dynamic updates of \(\mathcal{D}\). Also, we give a compressed index for approximate dictionary matching with one error. In each case, the query time is only slowed down by a polylogarithmic factor when compared with that achieved by the best O(n)-word counterparts.

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Fig. 1
Algorithm 1
Algorithm 2

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Notes

  1. In fact, Chan et al.’s index can support dynamic updates of \(\mathcal{D}\).

  2. A predecessor query reports the largest integer in the set that is at most the query integer, while a successor query reports the smallest integer in the set that is at least the query integer.

  3. Here, node insertion includes the case where a node is inserted into the middle of an existing edge, thus splitting one edge into two edges. On the other hand, when a degree-1 internal node is deleted, we reverse the process so that its parent edge and its child edge will be merged to a single edge.

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Authors and Affiliations

  1. National Tsing Hua University, Hsinchu City, Hsinchu, Taiwan, Republic of China

    Wing-Kai Hon & Tsung-Han Ku

  2. The University of Hong Kong, Hong Kong, Hong Kong SAR

    Tak-Wah Lam & Siu-Lung Tam

  3. Louisiana State University, Baton Rouge, LA, USA

    Rahul Shah & Sharma V. Thankachan

  4. The University of Kansas, Lawrence, KS, USA

    Jeffrey Scott Vitter

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  1. Wing-Kai Hon
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  2. Tsung-Han Ku
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  3. Tak-Wah Lam
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  4. Rahul Shah
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  5. Siu-Lung Tam
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  6. Sharma V. Thankachan
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  7. Jeffrey Scott Vitter
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Correspondence to Wing-Kai Hon.

Additional information

This work is supported in part by Taiwan NSC Grant 99-2221-E-007-123 (W.K. Hon), HK RGC Grant HKU 7140/06E (T.W. Lam), and US NSF Grant CCF-1017623 (R. Shah and J.S. Vitter). A preliminary version of this work appears in the following conference proceedings: the Proceedings of the IEEE Data Compression Conference (DCC), 2008 and 2011, and the Proceedings of the International Symposium on Algorithms and Computation (ISAAC), 2009.

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Hon, WK., Ku, TH., Lam, TW. et al. Compressing Dictionary Matching Index via Sparsification Technique. Algorithmica 72, 515–538 (2015). https://doi.org/10.1007/s00453-013-9863-3

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