Support for implicit graphs

[milasudril]

Also a usecase for Dijkstra: https://github.com/milasudril/cheapest_route. In this case the graph is implicit. In particular, it will use 32 outgoing search directions. Also, it is not interesting to find the cost from the start pixel to every other pixel. You would rather pick a few pairs, and let the algorithm find a natural way connecting the vertices.

If you had to construct a graph using an adjacency list, you will most likely run out of memory. A solution to this is to make it possible somehow return the edges from a customization point, accepting a customized node id. In this case, the node id has to be the coordinates of the pixel. The cost function must be given two node id:s.

Searching the path to every point in the image is both space and time consuming. Thus, there must be a version of Dijkstra that stops at a requested vertex.

[lums658]

Having an implicit graph is part of the "bring you own graph" functionality that we intend to have for std::graph. Boost.Graph has this capability (see the knight's tour problem in the BGL book and on line https://www.boost.org/doc/libs/1_55_0/libs/graph/example/knights-tour.cpp).

The current interface definition for std::graph should be able to support this.

[dabrahams]

One challenge for these kinds of graphs is that the outgoing edges of a vertex often depend on previously-discovered vertices. That suggests some kind of memo is needed. You might not want to make that memo a part of the graph data structure, since then an “immutable” graph can't be safely shared across threads unless you add synchronization to the memo. It's worth thinking about how to accommodate this use case.