GSoC Report 2025: Sparse Polytope Sampling via Lazy Rounding

Author: Vladimir Necula

Organization: GeomScale
Mentors: Elias Tsigaridas, Matías Bender, Luca Perju

Overview

This report is the final deliverable for GSoC 2025, showcasing my contributions within GeomScale.

My work was focused on implementing and benchmarking a sparse variant of the billiard walk sampling algorithm, leveraging lazy Cholesky-based solutions while preserving sparsity throughout rounding and sampling operations. The work is intended to enable efficient sampling in high-dimensional convex polytopes with sparse constraints.

Pull Requests

Full GSoC Work/Implementation: Sparse Billiard Walk and Benchmark

Key Files:

  • Added: sparse_billiard_walk_benchmark.cpp – contains the implemented setup for testing and benchmarking the sparse billiard walk
  • Added: sparse_uniform_billiard_walk.h – implements the main logic of the sparse uniform billiard walk algorithm
  • Modified: hpolytope.h – adds integration of the newly implemented sparse walk functionalities

Acknowledgements

I would like to express my sincere gratitude to the GeomScale organization for providing me with this incredible opportunity to contribute to their project. Thus, I want to thank my project mentors, whose guidance and support were invaluable throughout this experience.

Lastly, I want to thank Google for organizing the Google Summer of Code program. It was an incredible experience and I am so grateful for it. Having the opportunity to be immersed in the world of open-source software development, while being mentored by members of impressive organizations was an invaluable experience that enhanced my theoretical and collaborative skills.