lapcpp
lapcpp solves dense linear assignment problems with a native
C++ implementation and a NumPy API. Python 3.9 or newer is required.
It exposes two solvers: lapjv and lapjv_batch.
lapcpp 1.0.0 derives from the lapjvh solver in LAPX 0.11.1.
Future solver development is led by lapcpp for C++ and laprust for Rust;
LAPX will incorporate their fixes and improvements.
It solves rectangular problems directly and handles unmatched rows and columns
implicitly when a finite cost_limit is supplied, without allocating an expanded
square cost matrix.
The square path uses Jonker–Volgenant initialization, reduction, and shortest
augmenting paths. This package is independent of LAPX and imports as lapcpp.
Installation
Once available on PyPI:
python -m pip install lapcpp
A source build requires a C++17 compiler and, for laprust, Rust/Cargo 1.83+
with a compatible target. Build dependencies (NumPy, Cython, setuptools) are
installed automatically by pip. NumPy is the only Python runtime dependency.
An installed wheel needs no compiler or Rust toolchain.
Quick start
import numpy as np
import lapcpp
cost = np.array([[3., 1.], [1., 4.]])
total, rows, cols = lapcpp.lapjv(cost)
# total = 2.0; rows = [0, 1]; cols = [1, 0]
costs = np.stack([cost, cost]) # (batch, rows, columns)
totals, rows, cols = lapcpp.lapjv_batch(costs, n_threads=2)
# totals = [2., 2.]; rows and cols are lists of arrays, one per problem
rectangular = np.array([[.1, .8, .9], [.9, .7, .8]], dtype=np.float32)
total, rows, cols = lapcpp.lapjv(rectangular, cost_limit=.5)
# Only (0, 0) is selected; total is about .1, excluding rejection penalties.
API
lapjv(cost, extend_cost=False, cost_limit=np.inf, return_cost=True,
*, precision="native", output="indices")
lapjv_batch(costs, extend_cost=False, cost_limit=np.inf, return_cost=True,
n_threads=0, *, precision="native", output="indices")
| Option | Behavior |
|---|---|
cost / costs |
Real numeric arrays with shape (N, M) / (B, N, M). |
extend_cost=True |
Allows rectangular inputs when the limit is infinite; no square padding is used. |
cost_limit |
A finite value permits unmatched endpoints, each charged cost_limit / 2 rounded to the selected cost dtype. Finite limits also permit rectangles and apply to square inputs. |
return_cost |
Defaults to True; totals sum selected original costs in float64 and exclude rejection penalties. False omits totals and skips the sum. |
precision |
"native" preserves float32/float64; other real numeric inputs use float64. Explicit "float32" / "float64" select working costs. |
output |
"indices" returns aligned row/column arrays; "pairs" returns (K, 2) arrays. |
n_threads |
Batch only. 0 / None selects automatically; negative values use one worker; positive values are capped by batch size. |
All solver paths use float64 potentials, distances and reduced-cost arithmetic,
while matrix storage follows precision. Finite-limit half-penalties retain
rounding in that selected cost dtype before search. This reduces cancellation
with float32 costs without widening the whole matrix. Extreme cost ranges and
cost conversion can still obscure small objective differences; this is not an
arbitrary-range exactness guarantee.
Rows are sorted and all returned indices are int64. They identify the selected pairs; unmatched items are absent. Batch results contain lists because each problem may select a different number of pairs. Equal-cost optima may return different assignments across solvers or precisions.
With a finite limit L, define h = cost_dtype(L/2), where cost_dtype is
the cost storage dtype selected by precision. The optimized objective is
sum(selected represented costs) + (N + M - 2*K) * h, where N and M
are the input dimensions and K is the number of selected pairs.
Represented costs are the input values after conversion to that cost dtype.
The reported total separately sums the selected original-input values in
float64 and excludes rejection penalties. It can differ from the represented-cost
sum when conversion rounds input values. Joint rejection is different from
solving a full assignment and then filtering high-cost pairs.
See API details for numerical and memory behavior.
Development and checks
python -m pip install -e ".[dev]"
cd tests
python -m pytest -q -m "not cross_package"
cd ..
python -m pytest -q .github/tests -m "not editable"
python -m build
The test suite covers SciPy and exhaustive-reference comparisons, rectangular and finite-limit cases, float32/float64, precision conversion, forbidden edges, empty inputs, invalid arguments, repeated workspaces, batch thread counts, concurrent calls, package independence, and type annotations. Historical LAPX regressions, cross-package concurrency, and isolated editable installs are also covered. See the solver test inventory, build and packaging checks, and CONTRIBUTING.md for commands and coverage.
Benchmarks
All three benchmark scripts compare SciPy (baseline), lapcpp, laprust, LAPX lapjvxa and LAPX lapjvsa. The LAPX candidates represent the JVX and JVS families using pair outputs, including their batch APIs. Once lapcpp and laprust are available on PyPI, install the dependencies below. Clone or download this repository for the scripts and run them from the repository root.
python -m pip install --upgrade lapcpp laprust "lapx==0.11.1" scipy
python benchmarks/benchmark_single.py --quick --repeats 3
python benchmarks/benchmark_batch.py --quick --threads 4 --repeats 3
python benchmarks/benchmark_tracking.py --quick --repeats 3
Use --json benchmark-results/run.json to save measurements and environment
details. Each solver is warmed right before its own sample, and calls repeat
until a sample lasts at least 10 ms; --reference-timing restores the pinned
LAPX timing. See benchmark methodology for full workloads,
reference LAPX settings, dedicated solver functions, tracking post-filtering, and
timing boundaries. Tracking never passes its threshold as solver cost_limit.
Paper
The solver, its implicit rejection, and its performance against SciPy and other Jonker–Volgenant implementations are described in Native Rectangular Linear Assignment with Implicit Rejection: A Jonker–Volgenant Solver without Square Expansion, where lapcpp is labeled JVCPP. Read the PDF; its scripts, raw results, and reproduction steps are in the lap-paper repository.
Automation and license
GitHub workflows test supported Python versions on Windows, Linux and macOS,
build and test source archives and wheels, and run the three benchmark modes.
Wheel builds are also available manually. A version tag triggers the release
workflow; PyPI publishing uses the repository's pypi environment and requires
its Trusted Publisher configuration. No releases are published by local builds.
MIT licensed. See LICENSE, NOTICE, and native-source license for attribution.
1 maintainer
Metadata
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