A PTAS for the square tiling problem

Authors:
Amihood Amir;Alberto Apostolico;Gad M. Landau;Oren Sar Shalom
Affiliations:
Bar-Ilan University, Israel and Johns Hopkins University;Georgia Tech and University of Padova, Italy;University of Haifa, Israel, and NYU-Poly;Bar-Ilan University, Israel
Venue:
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
Year:
2010

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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 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 - ε/2 log n) for any given ε ≤ 1.