A PTAS for the Square Tiling Problem

Amihood Amir, Alberto Apostolico, Gad M. Landau, Ely Porat, Oren Sar Shalom

Research output: Contribution to journalArticlepeer-review


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 for any given ε ≤ 1. Another topic handled in this paper is the NP-hardness of the Tiling problem with an infinite alphabet. We show that when the alphabet is not bounded, even the decision version for rectangles of size 3. n is NP-Complete.

Original languageEnglish
Pages (from-to)33-45
Number of pages13
JournalTheoretical Computer Science
Issue numberC
StatePublished - 2015

Bibliographical note

Publisher Copyright:
© 2014 Elsevier B.V.


  • Finite alphabets
  • NP-Hardness
  • Two dimensional tiling

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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