Version 5.0 The LEDA User Manual

template
bool ALL PAIRS SHORTEST PATHS T(graph& G, const edge array& c,
node matrix& DIST)
returns true if G has no negative cycle and returns false otherwise.
In the latter case all values returned in DIST are
unspecified. In the former case the following holds for all v
and w: if µ(v, w) < ∞ then DIST(v, w) = µ(v, w) and if
µ(v, w) = ∞ then the value of DIST(v, w) is arbitrary. The
procedure runs in time O(nm + n 2 log n).
rational MINIMUM RATIO CYCLE(graph& G, const edge array& c,
const edge array& p, list& C star)
Returns a minimum cost to profit ratio cycle C star and the
ratio of the cycle. For a cycle C let c(C) be the sum of the c-
values of the edges on the cycle and let p(C) be the sum of the
p-values of the edges on the cycle. The cost to profit ratio of
the cycle is the quotient c(C)/p(C). The cycle C start realizes
the minimum ratio for any cycle C. The procedure runs in
time O(nm log(n · C · P )) where C and P are the maximum
cost and profit of any edge, respectively. The program returns
zero if there is no cycle in G.
Precondition: There are no cycles of cost zero or less with
respect to either c or p.