  This article presents a simplification of Zadimoghaddam's algorithm for the
edge-weighted online bipartite matching problem, under the online primal dual
framework. In doing so, we obtain an improved competitive ratio of $0.514$. We
first combine the online correlated selection (OCS), an ingredient distilled
from Zadimoghaddam (2017) by Huang and Tao (2019), and an interpretation of the
edge-weighted online bipartite matching problem by Devanur et al. (2016) which
we will refer to as the complementary cumulative distribution function (CCDF)
viewpoint, to derive an online primal dual algorithm that is
$0.505$-competitive. Then, we design an improved OCS which gives the $0.514$
ratio.
