All Pairs Shortest Paths Algorithms
Let G be a directed graph and cost a cost function
on the edges of G. Edge costs may be positive or negative.
An all pairs source shortest paths algorithm computes the shortest
paths between all pairs of nodes in G with respect to cost.
ALL_PAIRS_SHORTEST_PATHS_T() is the LEDA function
for computing the lengths of the shortest paths between all pairs of nodes
in a directed graph. ALL_PAIRS_SHORTEST_PATHS_T() is a template
function. The template parameter NT can be instantiated with
any number type.
Example of How to Use
ALL_PAIRS_SHORTEST_PATHS_T()
ALL_PAIRS_SHORTEST_PATHS() is the name of the preinstantiated
versions of ALL_PAIRS_SHORTEST_PATHS_T(). There is one function
ALL_PAIRS_SHORTEST_PATHS() for edge costs of type int
and one for double.
Example of How to Use ALL_PAIRS_SHORTEST_PATHS()
Important Notice: ALL_PAIRS_SHORTEST_PATHS() only performs correctly
if all arithmetic is performed without rounding errors and without overflows.
If you are not sure about this, you should use ALL_PAIRS_SHORTEST_PATHS_T()
with one of the LEDA number types.
Running time
The running time of ALL_PAIRS_SHORTEST_PATHS_T() and ALL_PAIRS_SHORTEST_PATHS()
for a graph G=(V,E) is O(|V||E|+|V|2log|V|).
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