In this paper we introduce a new family of string processing problems. We are given two or more strings and we are asked to compute a factor common to all strings that preserves a specific property and has maximal length. Here we consider two fundamental string properties: square-free factors and periodic factors under two different settings, one per property. In the first setting, we are given a string x and we are asked to construct a data structure over x answering the following type of on-line queries: given string y, find a longest square-free factor common to x and y. In the second setting, we are given k strings and an integer 1<k′≤k and we are asked to find a longest periodic factor common to at least k′ strings. We present linear-time solutions for both settings. We anticipate that our paradigm can be extended to other string properties.
Ayad, L., Bernardini, G., Grossi, R., Iliopoulos, C., Pisanti, N., Solon, P., et al. (2018). Longest Property-Preserved Common Factor. In String Processing and Information Retrieval (pp.42-49) [10.1007/978-3-030-00479-8_4].
Longest Property-Preserved Common Factor
Bernardini, G;
2018
Abstract
In this paper we introduce a new family of string processing problems. We are given two or more strings and we are asked to compute a factor common to all strings that preserves a specific property and has maximal length. Here we consider two fundamental string properties: square-free factors and periodic factors under two different settings, one per property. In the first setting, we are given a string x and we are asked to construct a data structure over x answering the following type of on-line queries: given string y, find a longest square-free factor common to x and y. In the second setting, we are given k strings and an integer 1
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