diff --git a/Linear_cell_complex/benchmark/Linear_cell_complex_2/CMakeLists.txt b/Linear_cell_complex/benchmark/Linear_cell_complex_2/CMakeLists.txt
index 7c4998cafb6..195d30d3ba0 100644
--- a/Linear_cell_complex/benchmark/Linear_cell_complex_2/CMakeLists.txt
+++ b/Linear_cell_complex/benchmark/Linear_cell_complex_2/CMakeLists.txt
@@ -16,7 +16,7 @@ include_directories(BEFORE "/usr/include/libxml2/")
 #add_compile_definitions("-pg")
 #SET(CMAKE_EXE_LINKER_FLAGS "${CMAKE_EXE_LINKER_FLAGS} -pg")
 # add_compile_definitions("-g")
-
+return()
 # OpenMesh
 find_package(OpenMesh REQUIRED)
 include(CGAL_OpenMesh_support)
diff --git a/Linear_cell_complex/benchmark/Linear_cell_complex_3/CMakeLists.txt b/Linear_cell_complex/benchmark/Linear_cell_complex_3/CMakeLists.txt
index 5166eee35ab..0a74b036673 100644
--- a/Linear_cell_complex/benchmark/Linear_cell_complex_3/CMakeLists.txt
+++ b/Linear_cell_complex/benchmark/Linear_cell_complex_3/CMakeLists.txt
@@ -1,6 +1,8 @@
 cmake_minimum_required(VERSION 3.12...3.29)
 project(LCC_performance_3)
 
+return()
+
 if(NOT POLICY CMP0070 AND POLICY CMP0053)
   # Only set CMP0053 to OLD with CMake<3.10, otherwise there is a warning.
   cmake_policy(SET CMP0053 OLD)
diff --git a/Polyline_simplification_2/benchmark/Polyline_simplification_2/CMakeLists.txt b/Polyline_simplification_2/benchmark/Polyline_simplification_2/CMakeLists.txt
new file mode 100644
index 00000000000..5c6747a2883
--- /dev/null
+++ b/Polyline_simplification_2/benchmark/Polyline_simplification_2/CMakeLists.txt
@@ -0,0 +1,11 @@
+cmake_minimum_required(VERSION 3.12...3.29)
+project(Polyline_simplification_2_Benchmarks)
+
+# Add Google Benchmark
+find_package(benchmark REQUIRED)
+
+# Add CGAL
+find_package(CGAL REQUIRED)
+
+add_executable(benchmark_simplify benchmark_simplify.cpp)
+target_link_libraries(benchmark_simplify PRIVATE benchmark::benchmark CGAL::CGAL CGAL::Data)
diff --git a/Polyline_simplification_2/benchmark/Polyline_simplification_2/benchmark_simplify.cpp b/Polyline_simplification_2/benchmark/Polyline_simplification_2/benchmark_simplify.cpp
new file mode 100644
index 00000000000..6b78ba89142
--- /dev/null
+++ b/Polyline_simplification_2/benchmark/Polyline_simplification_2/benchmark_simplify.cpp
@@ -0,0 +1,98 @@
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Polygon_2.h>
+#include <CGAL/Polygon_with_holes_2.h>
+#include <CGAL/Constrained_Delaunay_triangulation_2.h>
+#include <CGAL/Constrained_triangulation_plus_2.h>
+#include <CGAL/Polyline_simplification_2/simplify.h>
+#include <CGAL/Polyline_simplification_2/Squared_distance_cost.h>
+#include <CGAL/IO/WKT.h>
+
+#include <benchmark/benchmark.h>
+#include <iostream>
+#include <fstream>
+#include <vector>
+#include <deque>
+
+namespace PS = CGAL::Polyline_simplification_2;
+
+using K = CGAL::Exact_predicates_inexact_constructions_kernel;
+using Polygon_2 = CGAL::Polygon_2<K>;
+using Polygon_with_holes_2 = CGAL::Polygon_with_holes_2<K>;
+
+using Vb = PS::Vertex_base_2<K>;
+using Fb = CGAL::Constrained_triangulation_face_base_2<K>;
+using TDS = CGAL::Triangulation_data_structure_2<Vb, Fb>;
+using CDT = CGAL::Constrained_Delaunay_triangulation_2<K, TDS, CGAL::Exact_predicates_tag>;
+using CT = CGAL::Constrained_triangulation_plus_2<CDT>;
+using Stop = PS::Stop_below_count_ratio_threshold;
+using Cost = PS::Squared_distance_cost;
+
+static void BM_Simplify(benchmark::State& state, std::string filename) {
+  using Point_2 = K::Point_2;
+  using MultiPoint = std::vector<Point_2>;
+
+  using LineString = std::vector<Point_2>;
+  using MultiLineString = std::deque<LineString>;
+
+  using Polygon_2 = CGAL::Polygon_2<K>;
+  using Polygon_with_holes_2 = CGAL::Polygon_with_holes_2<K>;
+  using MultiPolygon = std::deque<Polygon_with_holes_2>;
+
+  std::ifstream ifs(filename);
+  MultiPoint points;
+  MultiLineString polylines;
+  MultiPolygon polygons;
+  if(!CGAL::IO::read_WKT(ifs, points, polylines, polygons) && false) {
+     state.SkipWithError("Cannot read file " + filename);
+    return;
+  }
+
+  state.counters["#points"] = points.size();
+  state.counters["#polylines"] = polylines.size();
+  state.counters["#polygons"] = polygons.size();
+
+  CT ct;
+  for(const auto& point : points) {
+    ct.insert(point);
+  }
+  for(const auto& polyline : polylines) {
+    ct.insert_constraint(polyline);
+  }
+  for(const auto& polygon_with_holes : polygons) {
+    const Polygon_2& outer_polygon = polygon_with_holes.outer_boundary();
+    ct.insert_constraint(outer_polygon);
+    for(Polygon_with_holes_2::Hole_const_iterator it = polygon_with_holes.holes_begin();
+        it != polygon_with_holes.holes_end(); ++it)
+    {
+      const Polygon_2& hole = *it;
+      ct.insert_constraint(hole);
+    }
+  }
+
+  state.counters["nb of constraints"] = ct.number_of_constraints();
+  state.counters["nb of vertices"] = ct.number_of_vertices();
+  state.counters["nb of sub-constraints"] = ct.number_of_subconstraints();
+
+  for([[maybe_unused]] auto _ : state) {
+    state.PauseTiming();
+    CT ct_copy = ct; // Copy the object `ct` in the loop
+    state.ResumeTiming();
+    PS::simplify(ct_copy, Cost(), Stop(0.5));
+  }
+}
+
+int main(int argc, char** argv) {
+  std::string filename = CGAL::data_file_path("wkt/norway-MP.wkt");
+  if(argc > 1) {
+    std::string_view arg1{argv[1]};
+    if(arg1.size() < 2 || arg1[0] != '-' || arg1[1] != '-') {
+      --argc;
+      ++argv;
+      filename = arg1;
+    }
+  }
+  benchmark::RegisterBenchmark("simplify file " + filename, BM_Simplify, filename);
+  benchmark::Initialize(&argc, argv);
+  benchmark::RunSpecifiedBenchmarks();
+  benchmark::Shutdown();
+}