  In this paper we consider the problem of finding a maximum weight set subject
to a $k$-extendible constraint in the data stream model. The only non-trivial
algorithm known for this problem to date---to the best of our knowledge---is a
semi-streaming $k^2(1 + \varepsilon)$-approximation algorithm (Crouch and
Stubbs, 2014), but semi-streaming $O(k)$-approximation algorithms are known for
many restricted cases of this general problem. In this paper, we close most of
this gap by presenting a semi-streaming $O(k \log k)$-approximation algorithm
for the general problem, which is almost the best possible even in the offline
setting (Feldman et al., 2017).
