Version 5.0 The LEDA User Manual

GRAPH TRANSITIVE CLOSURE(const graph& G)
TRANSITIVE CLOSURE takes a directed graph G = (V, E) as argument
and computes the transitive closure of G. It returns a directed
graph G ′ = (V ′ , E ′ ) such that G’.inf (.) is a bijective mapping from V ′
to V and (v, w) ∈ E ′ ⇔ there is a path from G’.inf (v’) to G’.inf (w’) in
G. (The edge information of G ′ is undefined.) The algorithm ([40]) has
running time O(|V | · |E|).
GRAPH TRANSITIVE REDUCTION(const graph& G)
TRANSITIVE REDUCTION takes a directed graph G = (V, E) as argument
and computes the transitive reduction of G. It returns a directed
graph G ′ = (V ′ , E ′ ). The function G’.inf (.) is a bijective mapping from
V ′ to V . The graph G and G ′ have the same reachability relation, i.e.
there is a path from v ′ to w ′ in G ′ ⇔ there is a path from G’.inf (v’)
to G’.inf (w’) in G. And there is no graph with the previous property
and less edges than G ′ . (The edge information of G ′ is undefined.) The
algorithm ([40]) has running time O(|V | · |E|).
void MAKE TRANSITIVELY CLOSED(graph& G)
MAKE TRANSITIVELY CLOSED transforms G into its transitive closure
by adding edges.
void MAKE TRANSITIVELY REDUCED(graph& G)
MAKE TRANSITIVELY REDUCED transforms G into its transitive reduction
by removing edges.