Streaming Dictionary Matching with Mismatches

In the k-mismatch problem we are given a pattern of length n and text must find all locations where Hamming distance between is at most k. A series recent breakthroughs have resulted in an ultra-efficient streaming algorithm for this that requires only $$\mathcal {O}(k \log \frac{n}{k})$$ space {O}(\log \frac{n}{k} (\sqrt{k k} + ^3 n))$$ time per letter (Clifford, Kociumaka, Porat, SODA 2019). work, consider strictly harder called dictionary matching with k mismatches. problem, d patterns, each n, substrings within from one patterns. We develop ^k \mathop {\mathrm {polylog} {\,n}})$$ ^{k} {\,n}} |\mathrm {output}|)$$ position text. The randomised outputs correct answers high probability. On lower bound side, show any mismatches $$\varOmega (k d)$$ bits space.