Tomohiro I

The "runs" theorem

We give a new characterization of maximal repetitions (or runs) in strings based on Lyndon words. The characterization leads to a proof of what was known as the “runs” conjecture [R. M. Kolpakov an...

Counting Parameterized Border Arrays for a Binary Alphabet

The parameterized pattern matching problem is a kind of pattern matching problem, where a pattern is considered to occur in a text when there exists a renaming bijection on the alphabet with which the pattern can be transformed into a substring of the text. A parameterized border array (p-border array ) is an analogue of a border array of a standard string, which is also known as the failure function of the Morris-Pratt pattern matching algorithm. In this paper we present a linear time algorithm to verify if a given integer array is a valid p-border array for a binary alphabet. We also show a linear time algorithm to compute all binary parameterized strings sharing a given p-border array. In addition, we give an algorithm which computes all p-border arrays of length at most n , where n is a a given threshold. This algorithm runs in time linear in the number of output p-border arrays.

Verifying a parameterized border array in O(n 1.5 ) time

The parameterized pattern matching problem is to check if there exists a renaming bijection on the alphabet with which a given pattern can be transformed into a substring of a given text. A parameterized border array (p-border array) is a parameterized version of a standard border array, and we can efficiently solve the parameterized pattern matching problem using p-border arrays. In this paper we present an O(n1.5)-time O(n)-space algorithm to verify if a given integer array of length n is a valid p-border array for an unbounded alphabet. The best previously known solution takes time proportional to the n-th Bell number 1/eΣk=0∞kn/k!, and hence our algorithm is quite efficient.

Lightweight Parameterized Suffix Array Construction

We present a first algorithm for direct construction of parameterized suffix arrays and parameterized longest common prefix arrays for non-binary strings. Experimental results show that our algorithm is much faster than naive methods.

Beyond the Runs Theorem

Recently, a short and elegant proof was presented showing that a binary word of length

Computing Palindromic Factorizations and Palindromic Covers On-line

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Inferring strings from suffix trees and links on a binary alphabet

contains at most

Fully Dynamic Data Structure for LCE Queries in Compressed Space

n-3

Faster Lyndon factorization algorithms for SLP and LZ78 compressed text

runs. Here we show, using the same technique and a computer search, that the number of runs in a binary word of length

Lempel Ziv Computation in Small Space (LZ-CISS)

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