Faster Two Dimensional Scaled Matching
The rapidly growing need for analysis of digitized images in multimedia systems has lead to a variety of interesting problems in multidimensional pattern matching. One of the problems is that of scaled matching, finding all appearances of a pattern, proportionally enlarged according to an arbitrary real-sized scale, in a given text.
The best known algorithm for this problem uses techniques from dictionary matching to solve the problem in O(nm 3+n 2 m logm) time using O(nm 3+n 2) space, where the text is a two-dimensional n ×n array and the pattern is a two-dimensional m ×m array.
We present a new approach for solving the scaled matching problem improving both the running times and the space requirements. Our algorithm runs in O(n 2 m) time and uses O(n 2) space. This time includes the preprocessing (O(m 3) time and O(m 2) space), since the problem is only defined for m ≤n.
Unable to display preview. Download preview PDF.
- 5.Amir, A., Calinescu, G.: Alphabet independent and dictionary scaled matching. In: Hirschberg, D.S., Meyers, G. (eds.) CPM 1996. LNCS, vol. 1075, pp. 320–334. Springer, Heidelberg (1996)Google Scholar
- 10.Gabow, H.N., Bentley, J.L., Tarjan, R.E.: Scaling and related techniques for geometry problems. In: Proc. 16th ACM Symposium on Theory of Computing, vol. 67, pp. 135–143 (1984)Google Scholar