Roger-luo / EliminateGraphs.jl

Graph model for fast elimination

EliminateGraphs

Maximum independent set algorithms, e.g. branching, measure and conquer.

To develop

Type ] in a Julia REPL, then input

pkg> dev [e-mail]:GiggleLiu/EliminateGraphs.jl.git

To run an example

julia> using EliminateGraphs

julia> eg = rand_eg(60, 0.05);

julia> mis1(eg)  # naive branching algorithm with O(3^(n/3)) complexity.
julia> mis1(eg)  # sophisticated branching algorithm with O(1.2852^N) complexity.

Using EliminateGraph,

julia> p = K_eg(3,3)
EliminateGraph
  0  0  0  1  1  1
  0  0  0  1  1  1
  0  0  0  1  1  1
  1  1  1  0  0  0
  1  1  1  0  0  0
  1  1  1  0  0  0

julia> q = p \ Neighbors{CLOSED, 1}(3)
EliminateGraph
  0  0  ⋅  ⋅  ⋅  ⋅
  0  0  ⋅  ⋅  ⋅  ⋅
  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅
  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅
  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅
  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅

julia> nv(q), ne(q)
(2, 0)

julia> vertices(q)
2-element VertexIter{EliminateGraph}:
 1
 2

julia> neighbors(p, 3)
NeighborIter{OPEN,1,EliminateGraph}
(4, 5, 6)

References

• Exact Exponential Algorithms