Online and Dynamic Recognition of Squarefree Strings

The online squarefree recognition problem is to detect the first occurrence of a square in a string whose characters are provided as input one at a time. We present an efficient algorithm to solve this problem for strings over arbitrarily ordered alphabets. Its running time is O(n log n), where n is the ending position of the first square, which matches the running times of the fastest known algorithms for the analogous offline problem. We also present a very simple algorithm for a dynamic version of the problem over general alphabets in which we are initially given a squarefree string, followed by a series of updates, and the objective is to determine after each update if the resulting string contains a square and if so, report it and stop.

• Type: Conference
• Year: 2005
• Where: MFCS
• Authors: Jesper Jansson, Zeshan Peng
• Keywords: Analogous Offline Problem, MFCS 2005, Squarefree Recognition Problem, first Occurrence