Approximate Matching in the L _∞ Metric

Abstract

Let a text T=t ₀,...,t _{n − − 1} and a pattern P=p ₀,..., p _{m − − 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 $_{i+{\it j}}$–p _j |. 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.

Partially supported by GIF Young Scientists Program grant 2055-1168.6/2002.