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In this paper we give an algorithm for streaming $k$-edit approximate patternmatching which uses space $\widetilde{O}(k^2)$ and time $\widetilde{O}(k^2)$per arriving symbol. This improves substantially on the recent algorithm ofKociumaka, Porat and Starikovskaya (2022) which uses space $\widetilde{O}(k^5)$and time $\widetilde{O}(k^8)$ per arriving symbol. In the $k$-edit approximatepattern matching problem we get a pattern $P$ and text $T$ and we want toidentify all substrings of the text $T$ that are at edit distance at most $k$from $P$. In the streaming version of this problem both the pattern and thetext arrive in a streaming fashion symbol by symbol and after each symbol ofthe text we need to report whether there is a current suffix of the text withedit distance at most $k$ from $P$. We measure the total space needed by thealgorithm and time needed per arriving symbol.

Streaming $k$-edit approximate pattern matching via string decomposition