Inversions of size exactly p characterize when large digraphs become k-arc-strong, while at most p-sized inversions admit a (4k-2+ε)-approximation for the minimum number needed and are NP-hard and APX-hard to optimize.
Bang-Jensen, F
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FPT algorithms exist for k-Inversion on tournaments (generalized), block graphs, and general digraphs via treewidth parameterization.
The (≤p)-inversion diameter of any graph G is at most ceil(|E(G)| / floor(p/2)) + Ψ_p, where Ψ_p satisfies (p/4 - 3/2) ≤ Ψ_p ≤ p²/2, with improved linear-in-n bounds for trees and planar graphs.
citing papers explorer
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Increasing arc-connectivity by bounded- and fixed-size inversions
Inversions of size exactly p characterize when large digraphs become k-arc-strong, while at most p-sized inversions admit a (4k-2+ε)-approximation for the minimum number needed and are NP-hard and APX-hard to optimize.
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Parameterized algorithms for $k$-Inversion
FPT algorithms exist for k-Inversion on tournaments (generalized), block graphs, and general digraphs via treewidth parameterization.
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On the $(\leq p)$-inversion diameter of oriented graphs
The (≤p)-inversion diameter of any graph G is at most ceil(|E(G)| / floor(p/2)) + Ψ_p, where Ψ_p satisfies (p/4 - 3/2) ≤ Ψ_p ≤ p²/2, with improved linear-in-n bounds for trees and planar graphs.