Version 5.0 The LEDA User Manual

template
bool SHORTEST PATH T(const graph& G, node s, const edge array& c,
node array& dist, node array& pred)
SHORTEST PATH solves the single source shortest path
problem in the graph G(V, E) with respect to the source node
s and the cost-function given by the edge array c.
The procedure returns false if there is a negative cycle in G
that is reachable from s and returns true otherwise.
It runs in linear time on acyclic graph, in time O(m +
n log n) if all edge costs are non-negative, and runs in time
O(min(D, n)m) otherwise. Here D is the maximal number of
edges on any shortest path.
list COMPUTE SHORTEST PATH(const graph& G, node s, node t,
const node array& pred)
computes a shortest path from s to t assuming that pred stores
a valid shortest path tree with root s (as it can be computed
with the previous function). The returned list contains the
edges on a shortest path from s to t. The running time is
linear in the length of the path.
template
node array CHECK SP T(const graph& G, node s, const edge array& c,
const node array& dist,
const node array& pred)
checks whether the pair (dist, pred) is a correct solution to the
shortest path problem (G, s, c) and returns a node array
label with label[v] < 0 if v has distance −∞ (−2 for nodes
lying on a negative cycle and −1 for a node reachable from
a negative cycle), label[v] = 0 if v has finite distance, and
label[v] > 0 if v has distance +∞. The program aborts if the
check fails. The algorithm takes linear time.
template
void ACYCLIC SHORTEST PATH T(const graph& G, node s,
const edge array& c,
node array& dist, node array& pred)
solves the single source shortest path problem with respect to
source s. The algorithm takes linear time.
Precondition: G must be acyclic.
template
void DIJKSTRA T(const graph& G, node s, const edge array& cost,
node array& dist, node array& pred)
solves the shortest path problem in a graph with non-negative
edges weights.
Precondition: The costs of all edges are non-negative.