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On Identifying Minimal Absent and Unique Words: An Efficient Scheme

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Abstract

One of the basic tasks in genomic research is the analysis of a sequence. An absent word in a sequence is a substring that does not occur in the given sequence. Many studies looked into finding the shortest absent words, with some recent studies noting that longer absent words are also of interest. A simple extension of the shortest ones is impractical as the list tends to grow exponentially in the size of the sequence. A better choice is the minimal absent words, since these are known to grow linearly in the size of the sequence. An absent word is minimal if none of its proper factors is missing in the sequence. Similarly, it is (left-fixed) minimal unique if none of its proper prefixes is unique. In this paper we present an efficient algorithm that discovers all words up to a user-specified length that are either minimal absent or are left-fixed minimal unique in the input sequence. We employ a purely deterministic approach which guarantees nothing is overlooked. At each successive iteration, the algorithm works on larger words using a simple list structure for all the operations. Theoretically, the algorithm has a space complexity that is linear with the size of input sequence, while the time bound scales well with alphabet size. Experimental results using real biological sequences and randomly generated ones using different-sized alphabets show that the algorithm has a linearity in time behavior.

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Acknowledgments

We would like to thank the anonymous reviewers for their helpful comments.

Funding

This study was funded by a special fund in the research center of College of Computer and Information Sciences (CCIS) at King Saud University.

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  1. Department of Computer Science, College of Computer and Information Sciences, King Saud University, Riyadh, 11543, Saudi Arabia

    Aqil M. Azmi

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  1. Aqil M. Azmi
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Correspondence to Aqil M. Azmi.

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Aqil M. Azmi declare that he has no conflict of interest.

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All procedures followed were in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and with the Helsinki Declaration of 1975, as revised in 2008 (5). Additional informed consent was obtained from all patients for which identifying information is included in this article.

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This article does not contain any studies with human or animal subjects performed by the any of the authors.

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Azmi, A.M. On Identifying Minimal Absent and Unique Words: An Efficient Scheme. Cogn Comput 8, 603–613 (2016). https://doi.org/10.1007/s12559-016-9385-9

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  • DOI: https://doi.org/10.1007/s12559-016-9385-9

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