An O(n log n) algorithm for finding all repetitions in a string
Journal of Algorithms
Two-dimensional dictionary matching
Information Processing Letters
Multiple matching of rectangular patterns
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
A Constant Time Optimal Parallel Algorithm for Two-Dimensional Pattern Matching
SIAM Journal on Computing
Efficient string matching: an aid to bibliographic search
Communications of the ACM
Inplace run-length 2d compressed search
Theoretical Computer Science
Multiple Pattern Matching in LZW Compressed Text
DCC '98 Proceedings of the Conference on Data Compression
Inplace 2D matching in compressed images
Journal of Algorithms
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
Succinct 2D dictionary matching with no slowdown
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
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The dictionary matching problem seeks all locations in a text that match any of the patterns in a dictionary. In the compressed dictionary matching problem, the input is in compressed form. In this paper we introduce the 2-dimensional compressed dictionary matching problem in Lempel-Ziv compressed images, and present an efficient solution for patterns whose rows are all periodic. Given k patterns, each of (uncompressed) size m×m, and a text of (uncompressed) size n×n, all in 2D-LZ compressed form, our algorithm finds all occurrences of the patterns in the text. The algorithm is strongly inplace, i.e., the extra space it uses is proportional to the optimal compression of the dictionary, which is O(km). The preprocessing time of the algorithm is O(km2), linear in the uncompressed dictionary size, and the time for performing the search is linear in the uncompressed text size, independent of the dictionary size. Our algorithm is general in the sense that it can be used for any 2D compression scheme which can be sequentially decompressed in small space.