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Efficient Online String Matching Based on Characters Distance Text Sampling

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Abstract

Searching for all occurrences of a pattern in a text is a fundamental problem in computer science with applications in many other fields, like natural language processing, information retrieval and computational biology. Sampled string matching is an efficient approach recently introduced in order to overcome the prohibitive space requirements of an index construction, on the one hand, and drastically reduce searching time for the online solutions, on the other hand. In this paper we present a new algorithm for the sampled string matching problem, based on a characters distance sampling approach. The main idea is to sample the distances between consecutive occurrences of a given pivot character and then to search online the sampled data for any occurrence of the sampled pattern, before verifying the original text. From a theoretical point of view we prove that, under suitable conditions, our solution can achieve both linear worst-case time complexity and optimal average-time complexity. From a practical point of view it turns out that our solution shows a sub-linear behaviour in practice and speeds up online searching by a factor of up to 9, using limited additional space whose amount goes from 11 to 2.8% of the text size, with a gain up to 50% if compared with previous solutions.

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Notes

  1. Search speed of an online string matching algorithm may depend on the length of the pattern. Typical search speed of a fast solution, on a modern laptop computer, goes from 1 GB/s (in the case of short patterns) to 5 GB/s (in the case of very long patterns) [5].

  2. Search speed of a fast offline solution do not depend on the length of the text and is typically under 1 ms per query.

  3. According to their theoretical evaluation and their experimental results it turns out that, when searching on an English text, the best performance are obtained when the least 13 characters are removed from the original alphabet.

  4. In practical cases we can implement our solution with a block size \(k=256\), which allows to represent the elements of the sequence \(\dot{y}\) using a single byte. In such a case the assumption \(k\ge \sigma\) is plausible for any practical application.

  5. The Smart tool is available online for download at http://www.dmi.unict.it/~faro/smart/ or at https://github.com/smart-tool/smart.

  6. Specifically, the text buffer is the concatenation of two different texts: The King James version of the bible (3.9 MB) and The CIA world fact book (2.4 MB). The first 5MB of the resulting text buffer have been used in our experimental results.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Catania, viale A.Doria n.6, 95125, Catania, Italy

    Simone Faro & Francesco Pio Marino

  2. Dipartimento di Scienze Cognitive, Università di Messina, via Concezione n.6, 98122, Messina, Italy

    Arianna Pavone

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  1. Simone Faro
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  2. Francesco Pio Marino
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  3. Arianna Pavone
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Correspondence to Simone Faro.

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Faro, S., Marino, F.P. & Pavone, A. Efficient Online String Matching Based on Characters Distance Text Sampling. Algorithmica 82, 3390–3412 (2020). https://doi.org/10.1007/s00453-020-00732-4

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