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