Abstract
We introduce new types of approximate palindromes called single-arm-gapped palindromes (SAGPs). A SAGP contains a gap in either its left or right arm, which is in the form of either \(wguc u^R w^R\) or \(wuc u^Rgw^R\), where w and u are non-empty strings, \(w^R\) and \(u^R\) are their reversed strings respectively, g is a gap, and c is either a single character or the empty string. We classify SAGPs into two groups: those which have \(ucu^R\) as a maximal palindrome (type-1), and the others (type-2). We propose several algorithms to compute all type-1 SAGPs with longest arms occurring in a given string using suffix arrays, and them a linear-time algorithm based on suffix trees. We also show how to compute type-2 SAGPs with longest arms in linear time. We perform some preliminary experiments to evaluate practical performances of the proposed methods.
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- 1.
We modified a van Emde Boas tree implementation from https://code.google.com/archive/p/libveb/ so that it works with Visual C++.
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Acknowledgements
This work was funded by ImPACT Program of Council for Science, Technology and Innovation (Cabinet Office, Government of Japan), Tohoku University Division for Interdisciplinary Advance Research and Education, and JSPS KAKENHI Grant Numbers JP15H05706, JP24106010, JP26280003.
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Narisada, S., Diptarama, Narisawa, K., Inenaga, S., Shinohara, A. (2017). Computing Longest Single-arm-gapped Palindromes in a String. In: Steffen, B., Baier, C., van den Brand, M., Eder, J., Hinchey, M., Margaria, T. (eds) SOFSEM 2017: Theory and Practice of Computer Science. SOFSEM 2017. Lecture Notes in Computer Science(), vol 10139. Springer, Cham. https://doi.org/10.1007/978-3-319-51963-0_29
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