Benchmarks for Delaunay-Cech trifiltrations

Benchmarks for "Bifunction and Interlevel Delaunay Trifiltrations"

Alonso, A., Kerber, M., Lam, T., Lesnick, M., & Rathod, A. (2026). Bifunction and Interlevel Delaunay Trifiltrations.

This benchmark set is an extension of

Michael Kerber and Tung Lam. Benchmark data sets of minimal presentations of 2-parameter persistence modules [data set]. Graz University of Technology, 2025. doi:10.3217/rxedk-qyq77

The software used to generate the output is available at https://bitbucket.org/mkerber/function_delaunay.

Directory Structure

The benchmarks are organized into four batches, labeled 1 to 4. Each batch contains the following subfolders:

examples/pointclouds/ -- point clouds without a function (e.g., S2_2000)

examples/ -- point clouds with a scalar function (e.g., torus_density_2000)

examples_interlevel/ -- point clouds with an R^2-valued function (e.g., torus_density_2000), used for interlevel trifiltration computations

output/ -- output from computing the interlevel Delaunay-Cech trifiltrations

Prerequisites

Before compiling the software, ensure the following dependencies are installed and accessible:

CGAL -- install CGAL and ensure its include directory is located (e.g., /usr/include/CGAL)

Eigen -- download and install Eigen3; specify its include path during compilation (e.g., path_to_eigen3)

GUDHI -- download and install GUDHI; specify its include path during compilation (e.g., path_to_gudhi)

CMake -- version 3.1 or newer

Boost -- ensure Boost is accessible to the build system (e.g., /usr/include/boost on Linux)

Compiler -- C++ compiler with C++11 or newer support (e.g., GCC or Clang)

Build

mkdir build
cd build
cmake -DCGAL_DIR=/usr/include/CGAL -DCMAKE_BUILD_TYPE=Release -DEIGEN_INCLUDE_DIR=path_to_eigen3 -DGUDHI_INCLUDE_DIR=path_to_gudhi -DBOOST_ROOT=path_to_boost ..
make

Usage

To run the trifiltration, you need the flag--two-functions

./main --two-functions input_file output_file

To reproduce all experiments in the benchmark set, first compile the software from https://bitbucket.org/mkerber/function_delaunay and place the compiled main executable in the same directory as run_experiments.sh. Then run:

bash run_experiments.sh

The script iterates over all input files in examples_interlevel/ across all batches, runs main --two-functions on each, and writes the output log to the corresponding output/ folder. A memory limit of 48 GB per run is enforced; any process exceeding this limit is terminated. Point cloud sizes covered are 500, 1000, 2000, 4000, 8000, and 16000.

Contact

Tung Lam ([e-mail], SUNY Albany)