The paper shows fine-grained hardness for approximating reachability diameter in directed graphs, gives additive approximations for unweighted cases, and constant-factor approximations for bounded treewidth and width-bounded DAGs.
Shortcuts and transitive-closure spanners approximation.arXiv preprint arXiv:2502.08032
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A greedy algorithm matches recent optimal size/hopbound tradeoffs for shortcut sets and receives a new existential optimality proof for matching hopsets up to logarithmic factors.
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Revisiting Diameter in Directed Graphs
The paper shows fine-grained hardness for approximating reachability diameter in directed graphs, gives additive approximations for unweighted cases, and constant-factor approximations for bounded treewidth and width-bounded DAGs.
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Greedy Algorithms for Shortcut Sets and Hopsets
A greedy algorithm matches recent optimal size/hopbound tradeoffs for shortcut sets and receives a new existential optimality proof for matching hopsets up to logarithmic factors.