Many applications have a need for indexing unstructured data. It turns out that a similar ad-hoc method is being used in many of them - that of considering small particles of the data. In this paper we formalize this concept as a tiling problem and consider the efficiency of dealing with this model in the pattern matching setting. We present an efficient algorithm for the one-dimensional tiling problem, and the one-dimensional tiled pattern matching problem. We prove the two-dimensional problem is hard and then develop an approximation algorithm with an approximation ratio converging to 2. We show that other two-dimensional versions of the problem are also hard, regardless of the number of neighbors a tile has. © 2011 Elsevier B.V. All rights reserved.
Amir, A., & Paryenty, H. (2012). Towards a theory of patches. Journal of Discrete Algorithms, 12, 61–73. https://doi.org/10.1016/j.jda.2011.12.022