Allow finding hamiltonian circuits

[andybalaam]

This is an implementation of Frank Rubin's 1973 algorithm to compute Hamiltonian circuits in a directed graph.

It's O(n!) but it goes to great effort to reduce the speed at which execution time increases with n.

[ABorgna]

Hi.
The CI error is fixed in HEAD. Could you rebase your changes on the latest version ?

[andybalaam]

@ABorgna rebased and pushed, thanks.

[andybalaam]

@ABorgna hmm. The CI failed with the trait std::iter::IntoIterator is not implemented for &[({integer}, {integer}); 73]. Any idea why this works on my machine? Maybe I'm using a too-recent Rust version?

[ABorgna]

Yes, it breaks in rust 1.41 (the MSRV). Replacing &[...] with [...].iter() should do the trick.
You can also test it by changing the toolchain version locally: rustup override set 1.41 (and rustup override unset to go back).

Thanks for the implementation. I warn you that it will take some time to review :)

[andybalaam]

I warn you that it will take some time to review :)

Of course, I absolutely expect that, and will help any way I can.

[andybalaam]

I found a bug and am working on a fix, so marking this as draft for now.

[andybalaam]

To build with rust 1.41.0 I needed:

rustup override set 1.41
cargo update -p indexmap --precise 1.7.0
cargo test

Then later to revert back to normal rust:

rustup override unset

(And maybe something to undo the --precise from above too?)

For my own info, I discovered this by reading https://github.com/petgraph/petgraph/blob/master/.github/workflows/ci.yml

[andybalaam]

OK, 2 bugs fixed, and compatibility with Rust 1.41 done!

The bugs have reduced my confidence in the tests though, so I'd welcome any suggestions on how to be more sure we are well-covered.

Both bugs made us not emit circuits that did exist, which is the harder case to test for. One possibility is to compare the list of circuits generated in the simplest possible way (without any of the R1...F6 conditions) against the list generated using the conditions. This would only be possible for small graphs, but might give us more confidence that the conditions are not excluding valid circuits.