Abstract
We study the problem of identifying palindromes in compressed strings. The underlying compression scheme is called run-length encoding, which has been extensively studied and widely applied in diverse areas. Given a run-length encoded string \(\textsc{rle}(T)\), we show how to preprocess \(\textsc{rle}(T)\) to support efficient retrieval of the longest palindrome with a specified center position and a tolerated number of mismatches between its two arms. Let n be the number of runs of \(\textsc{rle}(T)\) and k be the tolerated number of mismatches. We present two algorithms for the problem, both with preprocessing time polynomial in the number of runs. The first algorithm, devised for small k, identifies the desired palindrome in O(logn + min {k,n}) time with O(nlogn) preprocessing time, while the second algorithm achieves O(log2 n) query time, independent of k, after O(n 2logn)-time preprocessing.
Partially supported by NSC grants 97-2221-E-002-097-MY3 and 98-2221-E-002-081-MY3 from the National Science Council, Taiwan.
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Chen, KY., Hsu, PH., Chao, KM. (2010). Identifying Approximate Palindromes in Run-Length Encoded Strings. In: Cheong, O., Chwa, KY., Park, K. (eds) Algorithms and Computation. ISAAC 2010. Lecture Notes in Computer Science, vol 6507. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17514-5_29
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