- Type Parameters:
V- the graph vertex type
E- the graph edge type
Iterator over the shortest paths (not required to be simple) between two vertices in a graph sorted by weight.
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 fail-fast. The results of such modifications are undefined.
First the shortest paths tree in the edge reversed graph starting at
sinkis 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
sinkcan be solely determined by a sub-sequence of its edges which are sidetracks.
Let $d(v)$ be the distance from $v$ to
sinkand $w()$ 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
The idea of the algorithm is to build a heap of sidetracks. This heap can be then traversed with breadth-first search in order to retrieve the implicit representations of the paths between
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
- 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.
- Semen Chudakov
All Methods Instance Methods Concrete Methods Modifier and Type Method Description
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait