Two-dimensional prefix string matching and covering on square matrices

International audienceTwo linear time algorithms are presented. One for determining, for every position in a given square matrix, the longest prefix of a given pattern (also a square matrix) that occurs at that position and one for computing all square covers of a given two-dimensional square matrix

String Covering: A Survey

The study of strings is an important combinatorial field that precedes the digital computer. Strings can be very long, trillions of letters, so it is important to find compact representations. Here we first survey various forms of one potential compaction methodology, the cover of a given string x, initially proposed in a simple form in 1990, but increasingly of interest as more sophisticated variants have been discovered. We then consider covering by a seed; that is, a cover of a superstring of x. We conclude with many proposals for research directions that could make significant contributions to string processing in future

Rectangular tile covers of 2D-strings

We consider tile covers of 2D-strings which are a generalization of periodicity of 1D-strings. We say that a 2D-string A is a tile cover of a 2D-string S if S can be decomposed into non-overlapping 2D-strings, each of them equal to A or to AT, where AT is the transpose of A. We show that all tile covers of a 2D-string of size N can be computed in O(N1+ε) time for any ε > 0. We also show a linear-time algorithm for computing all 1D-strings being tile covers of a 2D-string