Strip Examples

This repository contains Python code for constructing and studying strip worst-case examples for reduction algorithm used in topological data analysis. These examples are similar to Morozov's worst-case examples but instead of a construction inside a single triangle, they are constructed by adding triangles on a strip of base and fin triangles. The scripts generate these strip examples, compute boundary matrix reductions, and benchmark the runtime of several reduction variants.

Repository Layout

src/
  strip_create.py         Build a worst-case complex, compute matrices, and plot a persistence diagram
  strip_runtime.py        Benchmark reduction algorithms and save runtime plots
  strip_utilities.py      Shared helpers for drawing and matrix reduction
notebooks/
  run_create_batch.py     Generate batches of simplicial complex and persistence diagram images
  run_runtime_batch.py    Generate batches of runtime benchmark plots
  results_*               Generated output folders created by the scripts
requirements.txt
LICENSE
README.md

Requirements

• Python 3.11 recommended
• gudhi
• numpy
• networkx
• matplotlib

Install with pip:

pip install -r requirements.txt

Or with conda:

conda create -n strip-examples python=3.11 -y
conda activate strip-examples
conda install -c conda-forge gudhi numpy networkx matplotlib -y

Running the Scripts

Run all commands from the repository root.

Build One Example

python3 src/strip_create.py

This script:

• constructs a worst-case filtered simplicial complex for a chosen n
• prints the simplices and persistence pairs
• writes boundary matrix outputs to notebooks/results_strip_create/
• shows the simplicial complex and persistence diagram

To change the size of the example, edit n in the __main__ block of src/strip_create.py.

Run One Runtime Benchmark

python3 src/strip_runtime.py

Optional arguments:

python3 src/strip_runtime.py --t 30 --verbose

• --t: maximum n value used in the benchmark
• --verbose: print per-n timing information

This script saves runtime plots to notebooks/results_strip_runtime/.

Generate Batch Figures

python3 notebooks/run_create_batch.py
python3 notebooks/run_runtime_batch.py

These scripts use the non-interactive matplotlib backend and save outputs to:

• notebooks/results_create_batch/
• notebooks/results_runtime_batch/

Output Files

The repository scripts currently write generated files into notebooks/:

• notebooks/results_strip_create/
• notebooks/results_strip_runtime/
• notebooks/results_create_batch/
• notebooks/results_runtime_batch/

These directories contain generated artifacts rather than source code.

Notes

• src/strip_create.py currently uses a hard-coded n value in its main block.
• src/strip_runtime.py benchmarks three reduction variants: standard, twist, and look-ahead.
• The plotting scripts require a working matplotlib installation.

Paper Reference

This repository contains experiments for the manuscript:

• (submitted to arXiv)

Citation

If you use this repository, please cite the associated paper:

@misc{cetinYalcin2026strip,
  title         = {<Worst-Case Examples for the Computation of Persistent Homology>},
  author        = {Uzay Cetin and Ergun Yalcin},
  year          = {2026},
  archivePrefix = {arXiv},
  primaryClass  = {math.AT}
}

Authors

• Uzay Cetin
• Ergun Yalcin

License

This project is distributed under the license in LICENSE.