  Given two matroids $\mathcal{M}_1 = (V, \mathcal{I}_1)$ and $\mathcal{M}_2 =
(V, \mathcal{I}_2)$ over an $n$-element integer-weighted ground set $V$, the
weighted matroid intersection problem aims to find a common independent set
$S^{*} \in \mathcal{I}_1 \cap \mathcal{I}_2$ maximizing the weight of $S^{*}$.
In this paper, we present a simple deterministic algorithm for weighted matroid
intersection using $\tilde{O}(nr^{3/4}\log{W})$ rank queries, where $r$ is the
size of the largest intersection of $\mathcal{M}_1$ and $\mathcal{M}_2$ and $W$
is the maximum weight. This improves upon the best previously known
$\tilde{O}(nr\log{W})$ algorithm given by Lee, Sidford, and Wong [FOCS'15], and
is the first subquadratic algorithm for polynomially-bounded weights under the
standard independence or rank oracle models. The main contribution of this
paper is an efficient algorithm that computes shortest-path trees in weighted
exchange graphs.
