Identifying approximate palindromes in run-length encoded strings

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 , we show how to preprocess 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 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(n2 log n)-time preprocessing. © 2010 Springer-Verlag.