From 665e66f0c59009f5f228c8ef2bce7fdfffac15db Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Mathieu=20Besan=C3=A7on?= <mathieu.besancon@gmail.com>
Date: Thu, 25 Apr 2024 17:52:08 +0200
Subject: [PATCH 1/6] independent set

---
 docs/src/algorithms.md  |  9 ++++++++
 src/GraphsOptim.jl      |  1 +
 src/independent_set.jl  | 47 +++++++++++++++++++++++++++++++++++++++++
 test/independent_set.jl | 22 +++++++++++++++++++
 test/runtests.jl        |  4 ++++
 5 files changed, 83 insertions(+)
 create mode 100644 src/independent_set.jl
 create mode 100644 test/independent_set.jl

diff --git a/docs/src/algorithms.md b/docs/src/algorithms.md
index ad088f9..aed8f28 100644
--- a/docs/src/algorithms.md
+++ b/docs/src/algorithms.md
@@ -70,6 +70,15 @@ GraphsOptim.min_vertex_cover!
 
 Finds a subset $S \subset V$ of vertices of an undirected graph $G = (V,E)$ such that $\forall (u,v) \in E: u \in S \lor v \in S$
 
+## Maximum Weight Independent Set
+
+```@docs
+maximum_weight_independent_set
+GraphsOptim.maximum_weight_independent_set!
+```
+
+Finds a subset $S \subset V$ of vertices of maximal weight of an undirected graph $G = (V,E)$ such that $\forall (u,v) \in E: u \notin S \lor v \notin S$.
+
 ## Graph matching
 
 !!! danger "Work in progress"
diff --git a/src/GraphsOptim.jl b/src/GraphsOptim.jl
index dc03c46..29e7e55 100644
--- a/src/GraphsOptim.jl
+++ b/src/GraphsOptim.jl
@@ -34,5 +34,6 @@ include("graph_matching.jl")
 include("min_vertex_cover.jl")
 include("fractional_coloring.jl")
 include("shortest_path.jl")
+include("independent_set.jl")
 
 end
diff --git a/src/independent_set.jl b/src/independent_set.jl
new file mode 100644
index 0000000..12d0778
--- /dev/null
+++ b/src/independent_set.jl
@@ -0,0 +1,47 @@
+
+"""
+    maximum_independent_set!(model, g; var_name)
+
+Computes in-place in the JuMP model a maximum-weighted independent set of `g`.
+An optional `vertex_weights` vector can be passed to the graph, defaulting to uniform weights (computing a maximum size independent set).
+"""
+function maximum_weight_independent_set!(
+    model::Model, g::AbstractGraph; binary::Bool=true, var_name, vertex_weights=ones(nv(g))
+)
+    if is_directed(g)
+        throw(ArgumentError("The graph must not be directed"))
+    end
+    g_vertices = collect(vertices(g))
+    f = @variable(model, [g_vertices]; binary=binary, base_name=String(var_name))
+    model[Symbol(var_name)] = f
+    @constraint(
+        model,
+        covering_constraint[i=1:nv(g), j=1:nv(g); i ≠ j && has_edge(g, i, j)],
+        f[i] + f[j] <= 1,
+    )
+    @objective(model, Max, dot(f, vertex_weights))
+    return model
+end
+
+"""
+    maximum_weight_independent_set(g; optimizer, binary, vertex_weights)
+
+Computes a maximum-weighted independent set or stable set of `g`.
+"""
+function maximum_weight_independent_set(
+    g::AbstractGraph;
+    binary::Bool=true,
+    vertex_weights=ones(nv(g)),
+    optimizer=HiGHS.Optimizer,
+)
+    model = Model(optimizer)
+    set_silent(model)
+    maximum_weight_independent_set!(
+        model, g; binary=binary, vertex_weights=vertex_weights, var_name=:stable
+    )
+    optimize!(model)
+    @assert termination_status(model) == OPTIMAL
+    stable_variables = Vector(model[:stable])
+    stable_vertices = findall(v -> value(v) > 0.5, stable_variables)
+    return stable_vertices
+end
diff --git a/test/independent_set.jl b/test/independent_set.jl
new file mode 100644
index 0000000..5db97f7
--- /dev/null
+++ b/test/independent_set.jl
@@ -0,0 +1,22 @@
+using GraphsOptim
+using Graphs
+using Test
+
+g = Graphs.random_regular_graph(10, 5)
+
+for _ in 1:10
+    vertex_weights = rand(nv(g))
+    stable = GraphsOptim.maximum_weight_independent_set(g; vertex_weights=vertex_weights)
+    if length(stable) > 1
+        for idx in 1:(length(stable) - 1)
+            @test !Graphs.has_edge(g, stable[idx], stable[idx + 1])
+        end
+    end
+end
+
+g2 = complete_graph(3)
+add_vertex!(g2)
+add_edge!(g2, 3, 4)
+stable = GraphsOptim.maximum_weight_independent_set(g2)
+@test length(stable) == 2
+@test 4 in stable
diff --git a/test/runtests.jl b/test/runtests.jl
index 8811777..4773df1 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -44,6 +44,10 @@ using Test
         include("min_vertex_cover.jl")
     end
 
+    @testset verbose = true "Independent set" begin
+        include("independent_set.jl")
+    end
+
     @testset verbose = true "Fractional coloring" begin
         include("fractional_coloring.jl")
     end

From 7e42f9d5783454a1220bb503117bc9893151b30a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Mathieu=20Besan=C3=A7on?= <mathieu.besancon@gmail.com>
Date: Thu, 25 Apr 2024 17:58:38 +0200
Subject: [PATCH 2/6] import function

---
 src/GraphsOptim.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/GraphsOptim.jl b/src/GraphsOptim.jl
index 29e7e55..46bc544 100644
--- a/src/GraphsOptim.jl
+++ b/src/GraphsOptim.jl
@@ -6,7 +6,7 @@ A package for graph optimization algorithms that rely on mathematical programmin
 module GraphsOptim
 
 using Graphs: AbstractGraph, is_directed
-using Graphs: vertices, edges, nv, ne, src, dst, inneighbors, outneighbors
+using Graphs: vertices, edges, nv, ne, src, dst, inneighbors, outneighbors, has_edge
 using Graphs: complement, maximal_cliques
 using FillArrays: Zeros, Ones, Fill
 using HiGHS: HiGHS

From c091a130fbd36905ae335ed49c4eae9b661b2bc7 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Mathieu=20Besan=C3=A7on?= <mathieu.besancon@gmail.com>
Date: Thu, 25 Apr 2024 18:15:19 +0200
Subject: [PATCH 3/6] export function

---
 src/GraphsOptim.jl | 1 +
 1 file changed, 1 insertion(+)

diff --git a/src/GraphsOptim.jl b/src/GraphsOptim.jl
index 46bc544..b4e75bd 100644
--- a/src/GraphsOptim.jl
+++ b/src/GraphsOptim.jl
@@ -24,6 +24,7 @@ export min_cost_flow
 export min_cost_assignment
 export FAQ, GOAT, graph_matching
 export min_vertex_cover
+export maximum_independent_set
 export fractional_chromatic_number, fractional_clique_number
 export shortest_path
 

From b8bb4ae34b51dd88b3141d09a8758b526bff0198 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Mathieu=20Besan=C3=A7on?= <mathieu.besancon@gmail.com>
Date: Thu, 25 Apr 2024 18:25:13 +0200
Subject: [PATCH 4/6] fix export

---
 src/GraphsOptim.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/GraphsOptim.jl b/src/GraphsOptim.jl
index b4e75bd..ec187fd 100644
--- a/src/GraphsOptim.jl
+++ b/src/GraphsOptim.jl
@@ -24,7 +24,7 @@ export min_cost_flow
 export min_cost_assignment
 export FAQ, GOAT, graph_matching
 export min_vertex_cover
-export maximum_independent_set
+export maximum_weight_independent_set
 export fractional_chromatic_number, fractional_clique_number
 export shortest_path
 

From 0be9e46c1d325c9f8213cfcf1eabaaf99d876a66 Mon Sep 17 00:00:00 2001
From: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
Date: Fri, 26 Apr 2024 14:12:23 +0200
Subject: [PATCH 5/6] Add to objective

---
 src/independent_set.jl | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/src/independent_set.jl b/src/independent_set.jl
index 12d0778..39caf9e 100644
--- a/src/independent_set.jl
+++ b/src/independent_set.jl
@@ -19,7 +19,8 @@ function maximum_weight_independent_set!(
         covering_constraint[i=1:nv(g), j=1:nv(g); i ≠ j && has_edge(g, i, j)],
         f[i] + f[j] <= 1,
     )
-    @objective(model, Max, dot(f, vertex_weights))
+    obj = objective_function(model)
+    add_to_expression!(obj, dot(f, vertex_weights))
     return model
 end
 

From 4851bfe004b958b46d7f1a8317d773955f2e8425 Mon Sep 17 00:00:00 2001
From: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
Date: Fri, 26 Apr 2024 14:22:50 +0200
Subject: [PATCH 6/6] Objective max

---
 src/independent_set.jl | 1 +
 1 file changed, 1 insertion(+)

diff --git a/src/independent_set.jl b/src/independent_set.jl
index 39caf9e..8f7762a 100644
--- a/src/independent_set.jl
+++ b/src/independent_set.jl
@@ -21,6 +21,7 @@ function maximum_weight_independent_set!(
     )
     obj = objective_function(model)
     add_to_expression!(obj, dot(f, vertex_weights))
+    @objective(model, Max, obj)
     return model
 end