Fast Entropy-Bounded String Dictionary Look-Up with Mismatches

We revisit the fundamental problem of dictionary look-up with mismatches. Given a set (dictionary) of d strings of length m and an integer k, we must preprocess it into a data structure to answer the following queries: Given a query string Q of length m, find all strings in the dictionary that are at Hamming distance at most k from Q. Chan and Lewenstein (CPM 2015) showed a data structure for k = 1 with optimal query time O(m/w + occ), where w is the size of a machine word and occ is the size of the output. The data structure occupies O(w d log^{1+epsilon} d) extra bits of space (beyond the entropy-bounded space required to store the dictionary strings). In this work we give a solution with similar bounds for a much wider range of values k. Namely, we give a data structure that has O(m/w + log^k d + occ) query time and uses O(w d log^k d) extra bits of space