Efficient two-dimensional compressed matching

Abstract

Digitized images are known to be extremely space consuming. However, regularities in the images can often be exploited to reduce the necessary storage area. Thus, many systems store images in a compressed form. The authors propose that compression be used as a time saving tool, in addition to its traditional role of space saving. They introduce a new pattern matching paradigm, compressed matching. A text array T and pattern array P are given in compressed forms c(T) and c(P). They seek all appearances of P in T, without decompressing T. This achieves a search time that is sublinear in the size of the uncompressed text mod T mod . They show that for the two-dimensional run-length compression there is a O( mod c(T) mod log mod P mod + mod P mod ), or almost optimal algorithm. The algorithm uses a novel multidimensional pattern matching technique, two-dimensional periodicity analysis.<>