Optimal Exact and Fast Approximate Two Dimensional Pattern Matching Allowing Rotations

We give fast filtering algorithms to search for a 2– dimensional pattern in a 2–dimensional text allowing any rotation of the pattern. We consider the cases of exact and approximate matching under several matching models, improving the previous results. For a text of size n× n characters and a pattern of size m×m characters, the exact matching takes average time O(n log m/m), which is optimal. If we allow k mismatches of characters, then our best algorithm achieves O(nk log m/m) average time, for reasonable k values. For large k, we obtain an O(nk √ log m/m) average time algorithm. We generalize the algorithms for the matching model where the sum of absolute differences between characters is at most k. Finally, we show how to make the algorithms optimal in the worst case, achieving the lower bound Ω(nm).