TY - GEN

T1 - Two-dimensional pattern matching in linear time and small space

AU - Crochemore, Maxime

AU - Gąsieniec, Leszek

AU - Rytter, Wojciech

AU - Plandowski, Wojciech

PY - 1995

Y1 - 1995

N2 - We present the first known (alphabet independent) algorithm for two-dimensional pattern matching which works in linear time and small space simultaneously. The searching phase of our algorithm works in O(1) space and is followed by pattern preprocessing performed in O(log m) space. Up to now there was not known even any efficient sublinear space algorithm for this problem. The main tools in our algorithm are several 2-dimensional variations of deterministic sampling, originally used in parallel pattern matching: small, frame and wide samples. Another novel idea used in our algorithm is the technique of zooming sequences: the sequences of nonperiodic decreasing parts of the pattern (samples) of similar regular shapes. Their regularity allows to encode the zooming sequences in small memory (logarithmic number of bits) while nonperiodicity allows to make shifts (kill positions as candidates for a match) in a way amortizing the work. The preprocessing phase is recursive, its structure is similar to the linear time algorithm for the selection problem. The stack of the recursion consists of logarithmic number of integers. Our algorithm is rather complicated, but all known alphabet-independent linear time algorithms (even with unrestricted space) for 2d-matching are quite complicated, too.

AB - We present the first known (alphabet independent) algorithm for two-dimensional pattern matching which works in linear time and small space simultaneously. The searching phase of our algorithm works in O(1) space and is followed by pattern preprocessing performed in O(log m) space. Up to now there was not known even any efficient sublinear space algorithm for this problem. The main tools in our algorithm are several 2-dimensional variations of deterministic sampling, originally used in parallel pattern matching: small, frame and wide samples. Another novel idea used in our algorithm is the technique of zooming sequences: the sequences of nonperiodic decreasing parts of the pattern (samples) of similar regular shapes. Their regularity allows to encode the zooming sequences in small memory (logarithmic number of bits) while nonperiodicity allows to make shifts (kill positions as candidates for a match) in a way amortizing the work. The preprocessing phase is recursive, its structure is similar to the linear time algorithm for the selection problem. The stack of the recursion consists of logarithmic number of integers. Our algorithm is rather complicated, but all known alphabet-independent linear time algorithms (even with unrestricted space) for 2d-matching are quite complicated, too.

UR - http://www.scopus.com/inward/record.url?scp=84947719729&partnerID=8YFLogxK

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U2 - 10.1007/3-540-59042-0_72

DO - 10.1007/3-540-59042-0_72

M3 - Conference contribution

AN - SCOPUS:84947719729

SN - 3540590420

SN - 9783540590422

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 181

EP - 192

BT - STACS 1995 - 12th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings

A2 - Mayr, Ernst W.

A2 - Puech, Claude

PB - Springer Verlag

T2 - 12th Annual Symposium on Theoretical Aspects of Computer Science, STACS 1995

Y2 - 2 March 1995 through 4 March 1995

ER -