Approximate matching in the L∞ metric

• Authors: Ohad Lipsky;Ely Porat
• Venue: SPIRE'05 Proceedings of the 12th international conference on String Processing and Information Retrieval
• Year: 2005

Let a text T=t0,...,tn−−1 and a pattern P=p0,..., pm−−1, strings of natural numbers, be given. In the Approximate Matching in the L∞metric problem the output is, for every text location i, the L∞ distance between the pattern and the length m substring of the text starting at i, i.e. Max$_{j=0}^{m--1}$|t$_{i+{\it j}}$–pj|. We consider the Approximate k–L∞distance problem. Given text T and pattern P as before, and a natural number k the output of the problem is the L∞ distance of the pattern from the text only at locations i in the text where the distance is bounded by k. For the locations where the distance exceeds k the output is φ. We show an algorithm that solves this problem in O(n(k+log(min(m, |Σ|)))logm) time.