  This paper presents near-optimal deterministic parallel and distributed
algorithms for computing $(1+\varepsilon)$-approximate single-source shortest
paths in any undirected weighted graph.
  On a high level, we deterministically reduce this and other shortest-path
problems to $\tilde{O}(1)$ Minor-Aggregations. A Minor-Aggregation computes an
aggregate (e.g., max or sum) of node-values for every connected component of
some subgraph.
  Our reduction immediately implies:
  Optimal deterministic parallel (PRAM) algorithms with $\tilde{O}(1)$ depth
and near-linear work.
  Universally-optimal deterministic distributed (CONGEST) algorithms, whenever
deterministic Minor-Aggregate algorithms exist. For example, an optimal
$\tilde{O}(HopDiameter(G))$-round deterministic CONGEST algorithm for
excluded-minor networks.
  Several novel tools developed for the above results are interesting in their
own right:
  A local iterative approach for reducing shortest path computations "up to
distance $D$" to computing low-diameter decompositions "up to distance
$\frac{D}{2}$". Compared to the recursive vertex-reduction approach of [Li20],
our approach is simpler, suitable for distributed algorithms, and eliminates
many derandomization barriers.
  A simple graph-based $\tilde{O}(1)$-competitive $\ell_1$-oblivious routing
based on low-diameter decompositions that can be evaluated in near-linear work.
The previous such routing [ZGY+20] was $n^{o(1)}$-competitive and required
$n^{o(1)}$ more work.
  A deterministic algorithm to round any fractional single-source transshipment
flow into an integral tree solution.
  The first distributed algorithms for computing Eulerian orientations.
