Inplace 2D matching in compressed images

Authors:
Amihood Amir;Gad M. Landau;Dina Sokol
Affiliations:
AT&T Labs -- Research, Florham Park, NJ;Haifa University, Haifa, Israel and Polytechnic University, Brooklyn, NY;Bar-Ilan University, Ramat-Gan, Israel
Venue:
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2003

Citing 10
Cited 1

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Optimal two-dimensional compressed matching

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Randomized Efficient Algorithms for Compressed Strings: The Finger-Print Approach (Extended Abstract)

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Abstract

The compressed matching problem, defined in [1] is the problem of finding all occurrences of a pattern in a compressed text. In this paper we discuss the 2-dimensional compressed matching problem in Lempel-Ziv compressed images. Given a pattern of (uncompressed) size m × m, and a text of (uncompressed) size n × n, both in 2D-LZ compressed form, our algorithm finds all occurrences of P in T. The algorithm is strongly inplace, that is, the amount of extra space used is proportional to the best possible compression of a pattern of size m2. The best compression that the 2D-LZ technique can obtain for a file of size m2 is O(m). The time for performing the search is O(n2) and the preprocessing time is O(m3). Our algorithm is general in the sense that it can be used for any 2D compression which can be sequentially decompressed in small space.