readme

Author: matbesancon

README.md

@@ -6,3 +6,47 @@
 
 [![codecov](https://codecov.io/gh/JuliaGraphs/LightGraphsMatching.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/JuliaGraphs/LightGraphsMatching.jl)
 
+Matching algorithms on top of [LightGraphs](https://github.com/JuliaGraphs/LightGraphs).
+
+## Usage
+
+The results of any matching is returned as a `MatchingResult` struct
+containing the `mate` and `weight` fields.
+
+### Perfect matching
+
+```julia
+g =CompleteGraph(4)
+w =Dict{Edge,Float64}()
+w[Edge(1,3)] = 10
+w[Edge(1,4)] = 0.5
+w[Edge(2,3)] = 11
+w[Edge(2,4)] = 2
+w[Edge(1,2)] = 100
+
+# find the perfect matching of minimum weight
+match = minimum_weight_perfect_matching(g, w, 50)
+# match.mate[1] == 4
+# match.mate[4] == 1
+# match.mate[2] == 3
+# match.mate[3] == 2
+# match.weight ≈ 11.5
+```
+
+### Maximum weight matching
+
+A maximum weight matching is solved as a Linear Programming
+problem and requires a LP solver respecting the [MathProgBase](https://github.com/JuliaOpt/MathProgBase.jl) solver
+interface. See MathProgBase 
+[documentation](http://mathprogbasejl.readthedocs.io/en/latest/solvers.html) for more details.
+
+```julia
+using Cbc: CbcSolver #import a LP solver
+g = CompleteGraph(3)
+w = zeros(3,3)
+w[1,2] = 1
+w[3,2] = 1
+w[1,3] = 1
+match = maximum_weight_matching(g,CbcSolver(),w)
+# match.weight ≈ 1
+```