Two-dimensional periodicity and its applications

Amihood Amir, Gary Benson

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

59 Scopus citations

Abstract

String matching is rich with a variety of algorithmic tools. In contrast, multidimensional matching has a rather sparse set of techniques. This paper presents a new algorithmic technique for two-dimensional matching, that of periodicity analysis. Periodicity in strings has been used to solve string matching problems. The success of these algorithms suggests that periodicity can be as important a tool in multidimensional matching. However, multidimensional periodicity is not as simple as it is in strings and was not formally studied or used in pattern matching. This paper's main contribution is defining and analysing two-dimensional periodicity in rectangular arrays. In addition, we introduce a new pattern matching paradigm - Compressed Matching. A text array T and a pattern array P are given in compressed forms c(T) and c(P). We seek all appearances of P in T, without decompressing T. By using periodicity analysis, we show that for the two-dimensional run-length compression there is a O(|c(T)| log |P| + |P|), or almost optimal algorithm that can achieve a search time that is sublinear in the size of the text |T|.

Original languageEnglish
Title of host publicationProceedings of the 3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992
PublisherAssociation for Computing Machinery
Pages440-452
Number of pages13
ISBN (Electronic)089791466X
StatePublished - 1 Sep 1992
Externally publishedYes
Event3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992 - Orlando, United States
Duration: 27 Jan 199229 Jan 1992

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
VolumePart F129721

Conference

Conference3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992
Country/TerritoryUnited States
CityOrlando
Period27/01/9229/01/92

Bibliographical note

Funding Information:
String periodicity is an intuitively clear concept and the properties of a string period are simple and well understood. Two-dimensional periodicit,y, though, presents some difficulties. Periodicity in the pJane is easy to de- fine. However, we are seeking the period of a finite rectangle. The concept of a “smallest” period that defines _Y%Hege of Computing, Georgia I&tit ute of Technology. tially supported by NSF grant IRI-901 305.5. t Department, of Computer Science, University

Funding

String periodicity is an intuitively clear concept and the properties of a string period are simple and well understood. Two-dimensional periodicit,y, though, presents some difficulties. Periodicity in the pJane is easy to de- fine. However, we are seeking the period of a finite rectangle. The concept of a “smallest” period that defines _Y%Hege of Computing, Georgia I&tit ute of Technology. tially supported by NSF grant IRI-901 305.5. t Department, of Computer Science, University

FundersFunder number
National Science FoundationIRI-901 305.5

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