Static sparse graphs on > 65536 vertices

[ncohen]

On Sage-devel [1], Christian reported an humiliating error message :

sage: graphs.PathGraph(70000).diameter()       
...
ValueError: The graph backend contains more than 65535 nodes

This is because Sage's "static_sparse_graphs" are stored on unsigned short fields (and thus to 65536 vertices), and though this is a meaningful limitation for Sage's code to compute the "all pairs shortest path" (the distance between all pairs of vertices, i.e. a n^{2 matrix of integers), it does not make any sense to refuse to compute the diameter of such graphs.}

Soooooooooo this patch changes these "unsigned short" to 32-bits unsigned integers (and note more, because that already doubles the memory requires), which is also good to have when Simon is about to use the same data structure for combinatorial graphs, which can be huge.

I have to mention that this does not make "diameter" answer very fast either on instances with more than 65536 vertices :-/

sage: %time graphs.PathGraph(70000).diameter()
CPU times: user 132.41 s, sys: 0.16 s, total: 132.57 s
Wall time: 133.42 s
69999

But at least we can build them T_T

What this patch does:

• change the type of the static_sparse_graph data structure from ushort to uint32_t, as well as the functions that use it
• change the all_pairs_shortest_path_BFS function to first compute the distance on a int * array of length n. The values are then copied into the n^2 matrix of ushort if necessary. That's a loss of time, but it's either this or rewriting two versions of the function :-/
• remove a useless degree variable in the same function
• Some simplifications from place to place in the code

Nathann

[1] ​https://groups.google.com/d/msg/sage-devel/2AI1CNdDm6w/jHKh26pMzqcJ