A C++ reference implementation of exact spanning tree modulus, computed via Cunningham's algorithm — the algorithm of Albin, Kottegoda, and Poggi-Corradini, "An Exact-Arithmetic Algorithm for Spanning Tree Modulus," Networks 85(4), 412-424. See the Python package's discrete_modulus.spanning_tree_modulus module and the companion book's "Exact Spanning Tree Modulus" chapter for the underlying theory.

Scope

This is an independent reference implementation of the same underlying theory covered by python/ and the companion book — not a wrapper or set of bindings around the Python package. It mirrors the Python module's public shape (create_flow_graph, cunningham_min, graph_vulnerability, spanning_tree_modulus) where that made sense, but is otherwise a fresh, idiomatic C++/Boost.Graph implementation, not a line-for-line port.

Only the exact spanning-tree-modulus algorithm is implemented here so far — unlike python/, this does not (yet) have a C++ equivalent of algorithms.py's general matrix_modulus/modulus framework or the family-of-objects functors.

Layout

include/discrete_modulus/ — the header-only library:
- graphs.hpp — the Graph/FlowGraph type aliases, subgraph/component helpers, and demo graph generators.
- cunningham.hpp — the algorithm itself.
src/spt_mod.cpp — a CLI: spt_mod <prefix> reads <prefix>.edges and writes <prefix>.eta.
examples/ — sample graphs for the CLI (house, nested, random, celegans, in increasing order of size/runtime — with a Release build, random takes well under a minute, but celegans takes a few minutes).
test/ — the Catch2 test suite.
docs/Doxyfile — Doxygen config for the API reference.

Building

Requires CMake >= 3.20, a C++17 compiler, and Boost >= 1.74 (the graph component). On Debian/Ubuntu: sudo apt install cmake libboost-graph-dev (already present in the devcontainer image).

cmake -S . -B build -DCMAKE_BUILD_TYPE=Release

cmake --build build

This builds the spt_mod CLI and the test suite (set -DDISCRETE_MODULUS_BUILD_TESTS=OFF to skip the latter).

-DCMAKE_BUILD_TYPE=Release matters here more than it might for other projects: this is a CPU-bound combinatorial algorithm, and an unoptimized (default/Debug) build is dramatically slower — enough to make the larger bundled examples (random, celegans) impractically slow.

Running the tests

ctest --test-dir build --output-on-failure

Running the CLI

./build/spt_mod examples/house

cat examples/house.eta

writes examples/house.eta (already checked into this repo, so this is a quick way to confirm the build reproduces the recorded output).

Building the API reference

Requires Doxygen (and, optionally, Graphviz for diagrams). From docs/:

doxygen Doxyfile

generates docs/_site/html/.

CI

.github/workflows/cpp-test.yml — builds and runs the test suite on every change under cpp/.
.github/workflows/book.yml's build-cpp-docs job renders this API reference and publishes it alongside the book and the Python API reference, under reference/cpp/.