8 research outputs found
EERTREE: An Efficient Data Structure for Processing Palindromes in Strings
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.Comment: 21 pages, 2 figures. Accepted to IWOCA 201
The Number of Distinct Subpalindromes in Random Words
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→∞(n,k)/√n does not exist for any k ≥ 2, liminfn→∞(n,k)/ √n=Θ(1), and limsupn→∞(n,k)/ √n=Θ(k). Such a complicated behaviour stems from the asymmetry between the palindromes of even and odd length. We show that a similar, but much simpler, result on the expected number of squares in random words holds. We also provide some experimental data on the number of palindromic factors in random words
EERTREE: An efficient data structure for processing palindromes in strings
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. © 2017 Elsevier Lt
Palk is linear recognizable online
Given a language L that is online recognizable in linear time and space, we construct a linear time and space online recognition algorithm for the language L・Pal, where Pal is the language of all nonempty palindromes. Hence for every fixed positive k, Palk is online recognizable in linear time and space. Thus we solve an open problem posed by Galil and Seiferas in 1978. © Springer-Verlag Berlin Heidelberg 2015
Palindromic k-Factorization in Pure Linear Time
Given a string s of length n over a general alphabet and an integer k, the problem is to decide whether s is a concatenation of k nonempty palindromes. Two previously known solutions for this problem work in time O(kn) and O(nlog n) respectively. Here we settle the complexity of this problem in the word-RAM model, presenting an O(n)-time online deciding algorithm. The algorithm simultaneously finds the minimum odd number of factors and the minimum even number of factors in a factorization of a string into nonempty palindromes. We also demonstrate how to get an explicit factorization of s into k palindromes with an O(n)-time offline postprocessing