added shortest path LMO

.github/workflows/ci.yml

@@ -0,0 +1,45 @@
+name: CI
+on:
+  push:
+    branches: [master]
+  pull_request:
+    types: [opened, synchronize, reopened]
+jobs:
+  test:
+    name: Julia ${{ matrix.version }} - ${{ matrix.os }} - ${{ matrix.arch }} - ${{ github.event_name }}
+    runs-on: ${{ matrix.os }}
+    strategy:
+      fail-fast: false
+      matrix:
+        include:
+          - version: '1'
+            os: ubuntu-latest
+            arch: x64
+          - version: '1.6'
+            os: ubuntu-latest
+            arch: x64
+          - version: '1'
+            os: macOS-latest
+            arch: x64
+    steps:
+      - uses: actions/checkout@v2
+      - uses: julia-actions/setup-julia@v1
+        with:
+          version: ${{ matrix.version }}
+          arch: ${{ matrix.arch }}
+      - uses: actions/cache@v1
+        env:
+          cache-name: cache-artifacts
+        with:
+          path: ~/.julia/artifacts
+          key: ${{ runner.os }}-test-${{ env.cache-name }}-${{ hashFiles('**/Project.toml') }}
+          restore-keys: |
+            ${{ runner.os }}-test-${{ env.cache-name }}-
+            ${{ runner.os }}-test-
+            ${{ runner.os }}-
+      - uses: julia-actions/julia-buildpkg@v1
+      - uses: julia-actions/julia-runtest@v1
+      - uses: julia-actions/julia-processcoverage@v1
+      - uses: codecov/codecov-action@v1
+        with:
+          file: lcov.info

src/CombinatorialLinearOracles.jl

@@ -7,5 +7,6 @@ using GraphsMatching
 
 include("matchings.jl")
 include("spanning_tree.jl")
+include("shortest_path.jl")
 
 end

src/shortest_path.jl

@@ -0,0 +1,30 @@
+
+struct ShortestPathLMO{T,G} <: FrankWolfe.LinearMinimizationOracle
+    graph::G
+    src::Int
+    dst::Int
+    dist_matrix::SparseArrays.SparseMatrixCSC{T,Int}
+end
+
+function ShortestPathLMO(graph, src_node, dst_node)
+    @assert !Graphs.is_cyclic(graph)
+    @assert Graphs.has_path(graph, src_node, dst_node)
+    dist_matrix = spzeros(nv(graph), nv(graph))
+    return ShortestPathLMO{eltype(dist_matrix), typeof(graph)}(graph, src_node, dst_node, dist_matrix)
+end
+
+function FrankWolfe.compute_extreme_point(lmo::ShortestPathLMO, direction)
+    for (idx, edge) in enumerate(edges(lmo.graph))
+        lmo.dist_matrix[src(edge), dst(edge)] = direction[idx]
+    end
+    shortest_path_result = Set(Graphs.a_star(lmo.graph, lmo.src, lmo.dst, lmo.dist_matrix))
+    # resulting vertex as a BitVector
+    indicence_vector = falses(ne(lmo.graph))
+    for (idx, edge) in enumerate(edges(lmo.graph))
+        if edge in shortest_path_result
+            indicence_vector[idx] = 1
+            delete!(shortest_path_result, edge)
+        end
+    end
+    return indicence_vector
+end

test/runtests.jl

@@ -76,3 +76,23 @@ end
     end
     @test Graphs.is_tree(SimpleGraphFromIterator(tree))
 end
+
+@testset "Shortest path" begin
+    n = 200
+    Random.seed!(42)
+    for _ in 1:10
+        g = Graphs.random_orientation_dag(Graphs.complete_graph(n))
+        src_node = 1
+        dst_node = nv(g)
+        while !has_path(g, src_node, dst_node) || src_node == dst_node
+            src_node = rand(1:nv(g))
+            dst_node = rand(1:nv(g))
+        end
+        lmo = CombinatorialLinearOracles.ShortestPathLMO(g, src_node, dst_node)
+        for _ in 1:10
+            direction = randn(ne(g))
+            v = FrankWolfe.compute_extreme_point(lmo, direction)
+            @test sum(v) >= 1
+        end
+    end
+end