ALGORITHMS

Assignment tutorials

Hands-on Jupyter notebooks covering the linear assignment problem — from first principles through SORT-style object tracking.

Three progressive tutorials on the assignment family, targeting readers with Python/PyTorch experience but no prior knowledge of combinatorial optimisation.

Tutorial	Topic	Notebook
Fundamentals	What LAP is, why brute force fails, `assignment.solve`	`assignment/01_the_assignment_problem.py`
Backends and batching	Backend selection, 3-D batched solve, unpacked output	`assignment/02_backends_and_batching.py`
Object tracking	IoU cost matrix, SORT-style tracker, trajectory visualisation	`assignment/03_object_tracking.py`

Running the notebooks locally

# Install the notebooks dependency group
uv sync --extra cu128 --group notebooks

# Launch Jupyter Lab
jupyter lab notebooks/

# Re-render the docs pages from executed notebooks
nix run .#nb-render -- --family assignment

Notebooks are stored as jupytext percent-format .py files under notebooks/assignment/. nix run .#nb-render converts them to .ipynb, executes each one, and writes the output to these pages.

Choosing

A decision tree drawn from the 540-case benchmark sweep, with rules of thumb by problem size, cost distribution, and tracing requirement.

Fundamentals

What the linear assignment problem is, why brute force fails, and how to solve your first problem with torchmatch.assignment.solve.