Correctness

Reachability

The preservation check compares reachability in the original graph with reachability after adding shortcut edges. It is an exact relation, not a sampled quality score.

Shortest paths

The distance check computes an exact baseline with Dijkstra and compares it with the bounded-hop result under the supplied epsilon and hop limit. Unreachable vertices are excluded from the ratio comparison.

What tests do not prove

Passing tests do not prove a universal runtime improvement, a theorem for every untested graph family, or a particular parallel speedup. Those claims require their own assumptions and measurements.