Abstract
The Square Tiling Problem was recently introduced as equivalent to the problem of reconstructing an image from patches and a possible general-purpose indexing tool. Unfortunately, the Square Tiling Problem was shown to be \(\cal{NP}\)-hard. A 1/2-approximation is known.
We show that if the tile alphabet is fixed and finite, there is a Polynomial Time Approximation Scheme (PTAS) for the Square Tiling Problem with approximation ratio of \((1-{\epsilon\over 2\log n})\) for any given ε ≤ 1.
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Amir, A., Apostolico, A., Landau, G.M., Shalom, O.S. (2010). A PTAS for the Square Tiling Problem. In: Chavez, E., Lonardi, S. (eds) String Processing and Information Retrieval. SPIRE 2010. Lecture Notes in Computer Science, vol 6393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16321-0_11
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DOI: https://doi.org/10.1007/978-3-642-16321-0_11
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