Class EppsteinShortestPathIterator<V,E>
 Type Parameters:
V
 the graph vertex typeE
 the graph edge type
This implementation can only be used for directed simple graphs. Also for this iterator to work correctly the graph must not be modified during iteration. Currently there are no means to ensure that, nor to failfast. The results of such modifications are undefined.
First the shortest paths tree in the edge reversed graph starting at sink
is built. Thus
we get distances $d(v)$ from every vertex $v$ to sink
. We then define a sidetrack edge to
be an edge, which is not in the shortest paths tree. The key observation is that every path
between the source
and the sink
can be solely determined by a subsequence of its
edges which are sidetracks.
Let $d(v)$ be the distance from $v$ to sink
and $w()$ be the weight function for edges in
graph
. If $e$ connects a pair of vertices $(u, w)$, the $\delta(e)$ is defined as
$w(e)+d(w)d(u)$. Intuitively, $\delta(e)$ measures how much distance is lost by being
“sidetracked” along $e$ instead of taking a shortest path to sink
.
The idea of the algorithm is to build a heap of sidetracks. This heap can be then traversed with
breadthfirst search in order to retrieve the implicit representations of the paths between
source
and sink
.
This implementation has several improvements in comparison to the original description in the article:
 An outgoing edge of vertex $v$ is inserted in the paths graph iff it is reachable from the
source
.  The cross edges in the paths graph are added only for those vertices which are reachable from the root vertex.
 Weights of the edges in the paths graph are mot maintained explicitly, because they are computed during its traversal.
 Author:
 Semen Chudakov

Constructor Details

EppsteinShortestPathIterator
Constructs an instance of the algorithm for the givengraph
,source
andsink
. Parameters:
graph
 graphsource
 source vertexsink
 sink vertex


Method Details