Towards a theory of patches

Amihood Amir, Haim Paryenty

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)61-73
Number of pages13
JournalJournal of Discrete Algorithms
StatePublished - Apr 2012


FundersFunder number
National Science Foundation0904581


    • Multi-dimensional indexing
    • Patches
    • Tiling


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