Lower bounds for text indexing with mismatches and differences

In this paper we study lower bounds for the fundamental problem of text indexing with mismatches and differences. In this problem we are given a long string of length n, the "text", and the task is to preprocess it into a data structure such that given a query string Q, one can quickly identify substrings that are within Hamming or edit distance at most k from Q. This problem is at the core of various problems arising in biology and text processing.