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 solves rectangular problems directly. With a finite cost_limit, it
handles unmatched rows and columns implicitly. Neither operation allocates 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.
The original lapcpp 1.0.0 release was derived from the lapjvh family in
LAPX 0.11.1.
lapcpp leads native solver development for C++.
laprust leads native solver development for
Rust. LAPX incorporates their fixes and improvements.
See the changelog for releases.
Installation
Install from PyPI:
python -m pip install lapcpp
Prebuilt wheels cover Python 3.9–3.15 on Windows, Linux and macOS. See the available files for platform and architecture coverage. NumPy is the only Python runtime dependency.
A source build requires a C++17 compiler. Pip installs the build dependencies (NumPy, Cython and setuptools) automatically. Installing a compatible wheel requires no compiler. See contributing for source builds.
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 |
These real numeric arrays have shape (N, M) / (B, N, M). |
extend_cost=True |
This option permits rectangular inputs when the limit is infinite. The solver does not use square padding. |
cost_limit |
A finite value permits unmatched rows and columns. Each unmatched row or column incurs cost_limit / 2, rounded to the selected cost dtype. Finite limits also permit rectangular inputs and apply to square inputs. |
return_cost |
The default is 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 the working cost dtype. |
output |
"indices" returns aligned row/column arrays. "pairs" returns (K, 2) arrays. |
n_threads |
This option applies only to batches. 0 / None selects the worker count 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. Float64 working arithmetic
reduces cancellation with float32 costs without widening the whole matrix.
Extreme cost ranges and cost conversion can still obscure small objective
differences. Float64 working
arithmetic does not guarantee exactness for arbitrary cost ranges.
Rows are sorted and all returned indices are int64. They identify the selected pairs. Unmatched rows and columns 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.
Here, N and M are the input dimensions. 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 these areas:
- Comparisons use SciPy and exhaustive references.
- Solver cases include rectangular and finite-limit problems, float32/float64, precision conversion, forbidden edges, empty inputs, and invalid arguments.
- Execution checks cover repeated workspaces, batch thread counts, concurrent calls, and cross-package concurrency.
- Package checks cover independence, type annotations, and isolated editable installs.
- Regression checks include historical LAPX cases.
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. Every mode requires LAPX 0.13.0 or newer. The LAPX candidates represent the JVX and JVS families using pair outputs, including their batch APIs. Clone or download this repository for the scripts. Run the scripts from the repository root with the released packages:
python -m pip install --upgrade lapcpp laprust "lapx>=0.13.0" scipy packaging
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
To benchmark this checkout, install python -m pip install -e ".[benchmark]"
instead. This command installs all comparison packages with the same LAPX
minimum version.
Use --json benchmark-results/run.json to save measurements and environment
details. Each solver receives a warm-up call immediately before its own sample.
Calibration chooses a repeat count that targets at least 10 ms per sample.
Measured durations can vary. --reference-timing uses the LAPX 0.13.0 benchmark
timing protocol.
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.
These package benchmarks use uniform random costs and JVS's default float32 working precision. The paper also covers structured, geometric, finite-limit, memory and application experiments. To reproduce those experiments, use the separate paper benchmark guide. That guide specifies its own workloads, precision settings and pinned environment.
Paper
The paper Native Rectangular Linear Assignment with Implicit Rejection: A Jonker–Volgenant Solver without Square Expansion describes the solver and its implicit rejection. It compares performance against SciPy and other Jonker–Volgenant implementations. The paper labels lapcpp JVCPP.
Read the current repository PDF or the arXiv preprint. The revised repository manuscript evaluates lapcpp/laprust 1.2.0 and LAPX 0.13.0 across four Windows/Linux and Python environments. The lap-paper repository includes the scripts, frozen evidence and reproduction steps. Its artifact guide explains how to regenerate figures and tables from the saved results.
Automation and license
GitHub workflows test supported Python versions on Windows, Linux and macOS.
The workflows also build and test source archives and wheels. Separate
workflows 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. Local builds do not publish releases.
lapcpp uses the MIT license. See LICENSE, NOTICE, and native-source license for attribution.
1 maintainer
Metadata
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