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We prove that a random word of length n over a k-ary fixed alphabet contains, on expectation, Θ( √ n) distinct palindromic factors. We study this number of factors, E(n, k), in detail, showing that the limit limn→∞ E(n, k)/ √ n does not exist for any k ≥ 2, lim infn→∞ E(n, k)/ √ n = Θ(1), and lim supn→∞ E(n, k)/ √ n = Θ( √ k). Such a complicated behaviour… (More)
We exhibit an online algorithm finding all distinct palindromes inside a given string in time Θ(n log |Σ|) over an ordered alphabet and in time Θ(n|Σ|) over an unordered alphabet. Using a reduction from a dictionary-like data structure, we prove the optimality of this algorithm in the comparison-based computation model.
We propose a new linear-size data structure which provides a fast access to all palindromic substrings of a string or a set of strings. This structure inherits some ideas from the construction of both the suffix trie and suffix tree. Using this structure, we present simple and efficient solutions for a number of problems involving palindromes.
Palindromic length of a string is the minimum number of palindromes whose concatenation is equal to this string. The problem of finding the palindromic length drew some attention, and a few O(n logn) time online algorithms were recently designed for it. In this paper we present the first linear time online algorithm for this problem. 1998 ACM Subject… (More)