Abstract
The Longest Common Extension of a pair of positions (i, j) in a string, or word, is the longest substring starting at i and j. The LCE problem considers a word and a set of pairs of positions and computes for each pair in the set, the longest common extension starting at both positions in the pair. This problem finds applications in matching with don’t-care characters, approximate string searching, finding all exact or approximate tandem repeats, to name a few. From a practical point of view, Ilie et al. (Journal of Discrete Algorithms, 2010) looked for simple and efficient algorithms for the LCE problem. In this paper, we extend their analyses to partial words, strings with don’t-cares or holes. In this context, we compute the Longest Common Compatible Extension of each pair of positions (i, j) in a partial word, i.e., the longest substrings starting at i and j that are compatible. We show that our results match with those of total words (partial words without holes). We find that one of the simplest algorithms for implementing the LCE problem is optimal on average in this case.
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Project sponsored by the National Security Agency under Grant Number H98230-15-1-0232. The United States Government is authorized to reproduce and distribute reprints notwithstanding any copyright notation herein. This manuscript is submitted for publication with the understanding that the United States Government is authorized to reproduce and distribute reprints. This material is based upon work supported by the National Science Foundation under Grant No. DMS–1060775.
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Blanchet-Sadri, F., Harred, R., Lazarow, J. (2016). Longest Common Extensions in Partial Words. In: Lipták, Z., Smyth, W. (eds) Combinatorial Algorithms. IWOCA 2015. Lecture Notes in Computer Science(), vol 9538. Springer, Cham. https://doi.org/10.1007/978-3-319-29516-9_5
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DOI: https://doi.org/10.1007/978-3-319-29516-9_5
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