Decision: how to applied to reduction to constrained topology

[GiggleLiu]

For example, we have the same problem defined on planar graph, unit-disk graph, tree graphs et al, instead of the most generic ones.

I suggest we define some wrapper types on the SimpleGraph type that defined in Graphs.jl.

Ref:

• https://github.com/QuEraComputing/UnitDiskMapping.jl

[hmyuuu]

It might be beneficial if we also wrap on SimpleEdgeIter type, and haveedges(g) return an iterator.

The point is that, we can check if an edge exists simply through a has_edge function without needing to generate all the edges again. c.f. Graphs.jl/

in(e, es::SimpleEdgeIter) = has_edge(es.g, e)

e.g. in the case of UnitDiskGraph, we can use

Graphs.has_edge(g::UnitDiskGraph, s, d) = sum(abs2, g.locations[s] .- g.locations[d]) ≤ g.radius^2

[hmyuuu]

Here are some benchmarks on my device with #34

julia> g = UnitDiskGraph([(0.0, 0.0), (1.0, 0.0), (0.0, 1.0), (1.0, 1.0)], 1.2)
UnitDiskGraph{2, Float64}([(0.0, 0.0), (1.0, 0.0), (0.0, 1.0), (1.0, 1.0)], 1.2)

julia> e = Graphs.SimpleEdge((3,4))
Edge 3 => 4

julia> @btime e in edges(g);
  28.907 ns (1 allocation: 32 bytes)

julia> @btime e in ProblemReductions.all_edges(g);
  83.462 ns (2 allocations: 208 bytes)

julia> @btime collect(edges(g));
  106.279 ns (4 allocations: 368 bytes)

julia> @btime ProblemReductions.all_edges(g);
  65.501 ns (2 allocations: 208 bytes)