Algorithms
A plain-language map of the two constructions reachq exposes: shortcut sets for reachability and hopsets for weighted shortest paths.
Shortcut sets
The reachability construction adds directed shortcut edges to make repeated traversal queries more structured. The supported correctness question is exact: does the augmented graph preserve reachability from every source?
Hopsets
The shortest-path construction adds weighted links intended to reduce the number of hops in approximate single-source shortest-path queries. Epsilon describes the error budget; the implementation and tests define the engineering behavior.
Research boundary
The implementation is informed by the cited paper, but a paper result, a reachq implementation detail, and an empirical benchmark are different claims. The provenance notes keep those categories separate.