The compressed matching problem 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 P of (uncompressed) size m × m, and a text T 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.
Bibliographical noteFunding Information:
* Corresponding author. E-mail addresses: email@example.com (A. Amir), firstname.lastname@example.org (G.M. Landau), email@example.com (D. Sokol). 1 Partially supported by NSF grant CCR-01-04494 and ISF grant 282/01. Part of this work was done when the author was at AT&T Labs-Research, Shannon Laboratory. 2 Partially supported by NSF grant CCR-0104307, by NATO Science Programme grant PST.CLG.977017, by the Israel Science Foundation grant 282/01, by the FIRST Foundation of the Israel Academy of Science and Humanities, and by IBM Faculty Partnership Award. 3 Partially supported by an Israel Ministry of Industry and Commerce Magnet grant (KITE) and an AT&T travel grant.
ASJC Scopus subject areas
- Control and Optimization
- Computational Mathematics
- Computational Theory and Mathematics