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lap: Linear Assignment Problem Solver

lap is a linear assignment problem solver using Jonker-Volgenant algorithm for dense LAPJV¹ or sparse LAPMOD² matrices. Both algorithms are implemented from scratch based solely on the papers¹˒² and the public domain Pascal implementation provided by A. Volgenant³. The LAPMOD implementation seems to be faster than the LAPJV implementation for matrices with a side of more than ~5000 and with less than 50% finite coefficients.

¹ R. Jonker and A. Volgenant, "A Shortest Augmenting Path Algorithm for Dense and Sparse Linear Assignment Problems", Computing 38, 325-340 (1987)
² A. Volgenant, "Linear and Semi-Assignment Problems: A Core Oriented Approach", Computer Ops Res. 23, 917-932 (1996)
³ http://www.assignmentproblems.com/LAPJV.htm | [archive.org]

💽 Installation

Install from PyPI:

PyPI version Downloads Downloads

pip install lap
PyPI Wheels 🛞 Windows ✅ Linux ✅ macOS ✅
Python 3.7 AMD64 x86_64/aarch64 x86_64
Python 3.8 AMD64 x86_64/aarch64 x86_64/arm64
Python 3.9-3.14 ¹ AMD64/ARM64 ² x86_64/aarch64 x86_64/arm64

¹ v0.5.13 supports both numpy 1.x and 2.x for Python 3.8-3.14. 🆕
² Windows ARM64 is experimental.

Other options

Install from GitHub repo (requires C++ compiler):

pip install git+https://github.com/gatagat/lap.git

Build and install (requires C++ compiler):

git clone https://github.com/gatagat/lap.git
cd lap
pip install "setuptools>=67.8.0"
pip install wheel build
python -m build --wheel
cd dist

🧪 Usage

import lap
import numpy as np
print(lap.lapjv(np.random.rand(4, 5), extend_cost=True))
More details

cost, x, y = lap.lapjv(C)

The function lapjv(C) returns the assignment cost cost and two arrays x and y. If cost matrix C has shape NxM, then x is a size-N array specifying to which column each row is assigned, and y is a size-M array specifying to which row each column is assigned. For example, an output of x = [1, 0] indicates that row 0 is assigned to column 1 and row 1 is assigned to column 0. Similarly, an output of x = [2, 1, 0] indicates that row 0 is assigned to column 2, row 1 is assigned to column 1, and row 2 is assigned to column 0.

Note that this function does not return the assignment matrix (as done by scipy's linear_sum_assignment and lapsolver's solve dense). The assignment matrix can be constructed from x as follows: A = np.zeros((N, M)) for i in range(N): A[i, x[i]] = 1

Equivalently, we could construct the assignment matrix from y:

A = np.zeros((N, M))
for j in range(M):
    A[y[j], j] = 1

Finally, note that the outputs are redundant: we can construct x from y, and vise versa:

x = [np.where(y == i)[0][0] for i in range(N)]
y = [np.where(x == j)[0][0] for j in range(M)]

License

Released under the 2-clause BSD license, see LICENSE.

Copyright (C) 2012-2025, Tomas Kazmar

Contributors (in alphabetic order):

  • Benjamin Eysenbach
  • Léo Duret
  • Pieter Lenaerts
  • Raphael Reme
  • Ratha Siv
  • Robert Wen
  • Steven
  • Tom White
  • Tomas Kazmar
  • Wok

Release files for lap 0.5.13

For a detailed explanation of source distributions (sdists) and built distributions (wheels), please see the package formats documentation.

Source distribution (sdist)

Source distribution for lap 0.5.13
File Size Uploaded
lap-0.5.13.tar.gz 1.5 MB Details

Built distributions (wheels)

Table of built distributions (wheels) for lap 0.5.13
File
lap-0.5.13-cp314-cp314-win_arm64.whl CPython 3.14 CPython 3.14 Windows ARM64 Details
lap-0.5.13-cp314-cp314-win_amd64.whl CPython 3.14 CPython 3.14 Windows x86-64 Details
lap-0.5.13-cp314-cp314-musllinux_1_2_x86_64.whl CPython 3.14 CPython 3.14 Linux musl 1.2+ x86-64 Details
lap-0.5.13-cp314-cp314-musllinux_1_2_aarch64.whl CPython 3.14 CPython 3.14 Linux musl 1.2+ ARM64 Details
lap-0.5.13-cp314-cp314-manylinux2014_aarch64.manylinux_2_17_aarch64.manylinux_2_28_aarch64.whl CPython 3.14 CPython 3.14 Linux glibc 2.17+ ARM64, Linux glibc 2.28+ ARM64 Details
lap-0.5.13-cp314-cp314-manylinux1_x86_64.manylinux_2_28_x86_64.manylinux_2_5_x86_64.whl CPython 3.14 CPython 3.14 Linux glibc 2.5+ x86-64, Linux glibc 2.28+ x86-64 Details
lap-0.5.13-cp314-cp314-macosx_11_0_arm64.whl CPython 3.14 CPython 3.14 macOS 11.0+ ARM64 Details
lap-0.5.13-cp314-cp314-macosx_10_15_x86_64.whl CPython 3.14 CPython 3.14 macOS 10.15+ x86-64 Details
lap-0.5.13-cp313-cp313-win_arm64.whl CPython 3.13 CPython 3.13 Windows ARM64 Details
lap-0.5.13-cp313-cp313-win_amd64.whl CPython 3.13 CPython 3.13 Windows x86-64 Details
lap-0.5.13-cp313-cp313-musllinux_1_2_x86_64.whl CPython 3.13 CPython 3.13 Linux musl 1.2+ x86-64 Details
lap-0.5.13-cp313-cp313-musllinux_1_2_aarch64.whl CPython 3.13 CPython 3.13 Linux musl 1.2+ ARM64 Details
lap-0.5.13-cp313-cp313-manylinux2014_aarch64.manylinux_2_17_aarch64.manylinux_2_28_aarch64.whl CPython 3.13 CPython 3.13 Linux glibc 2.17+ ARM64, Linux glibc 2.28+ ARM64 Details
lap-0.5.13-cp313-cp313-manylinux1_x86_64.manylinux_2_28_x86_64.manylinux_2_5_x86_64.whl CPython 3.13 CPython 3.13 Linux glibc 2.5+ x86-64, Linux glibc 2.28+ x86-64 Details
lap-0.5.13-cp313-cp313-macosx_11_0_arm64.whl CPython 3.13 CPython 3.13 macOS 11.0+ ARM64 Details
lap-0.5.13-cp313-cp313-macosx_10_13_x86_64.whl CPython 3.13 CPython 3.13 macOS 10.13+ x86-64 Details
lap-0.5.13-cp312-cp312-win_arm64.whl CPython 3.12 CPython 3.12 Windows ARM64 Details
lap-0.5.13-cp312-cp312-win_amd64.whl CPython 3.12 CPython 3.12 Windows x86-64 Details
lap-0.5.13-cp312-cp312-musllinux_1_2_x86_64.whl CPython 3.12 CPython 3.12 Linux musl 1.2+ x86-64 Details
lap-0.5.13-cp312-cp312-musllinux_1_2_aarch64.whl CPython 3.12 CPython 3.12 Linux musl 1.2+ ARM64 Details
lap-0.5.13-cp312-cp312-manylinux2014_aarch64.manylinux_2_17_aarch64.manylinux_2_28_aarch64.whl CPython 3.12 CPython 3.12 Linux glibc 2.17+ ARM64, Linux glibc 2.28+ ARM64 Details
lap-0.5.13-cp312-cp312-manylinux1_x86_64.manylinux_2_28_x86_64.manylinux_2_5_x86_64.whl CPython 3.12 CPython 3.12 Linux glibc 2.5+ x86-64, Linux glibc 2.28+ x86-64 Details
lap-0.5.13-cp312-cp312-macosx_11_0_arm64.whl CPython 3.12 CPython 3.12 macOS 11.0+ ARM64 Details
lap-0.5.13-cp312-cp312-macosx_10_13_x86_64.whl CPython 3.12 CPython 3.12 macOS 10.13+ x86-64 Details
lap-0.5.13-cp311-cp311-win_arm64.whl CPython 3.11 CPython 3.11 Windows ARM64 Details
lap-0.5.13-cp311-cp311-win_amd64.whl CPython 3.11 CPython 3.11 Windows x86-64 Details
lap-0.5.13-cp311-cp311-musllinux_1_2_x86_64.whl CPython 3.11 CPython 3.11 Linux musl 1.2+ x86-64 Details
lap-0.5.13-cp311-cp311-musllinux_1_2_aarch64.whl CPython 3.11 CPython 3.11 Linux musl 1.2+ ARM64 Details
lap-0.5.13-cp311-cp311-manylinux2014_aarch64.manylinux_2_17_aarch64.manylinux_2_28_aarch64.whl CPython 3.11 CPython 3.11 Linux glibc 2.28+ ARM64, Linux glibc 2.17+ ARM64 Details
lap-0.5.13-cp311-cp311-manylinux1_x86_64.manylinux_2_28_x86_64.manylinux_2_5_x86_64.whl CPython 3.11 CPython 3.11 Linux glibc 2.5+ x86-64, Linux glibc 2.28+ x86-64 Details
lap-0.5.13-cp311-cp311-macosx_11_0_arm64.whl CPython 3.11 CPython 3.11 macOS 11.0+ ARM64 Details
lap-0.5.13-cp311-cp311-macosx_10_9_x86_64.whl CPython 3.11 CPython 3.11 macOS 10.9+ x86-64 Details
lap-0.5.13-cp310-cp310-win_arm64.whl CPython 3.10 CPython 3.10 Windows ARM64 Details
lap-0.5.13-cp310-cp310-win_amd64.whl CPython 3.10 CPython 3.10 Windows x86-64 Details
lap-0.5.13-cp310-cp310-musllinux_1_2_x86_64.whl CPython 3.10 CPython 3.10 Linux musl 1.2+ x86-64 Details
lap-0.5.13-cp310-cp310-musllinux_1_2_aarch64.whl CPython 3.10 CPython 3.10 Linux musl 1.2+ ARM64 Details
lap-0.5.13-cp310-cp310-manylinux2014_aarch64.manylinux_2_17_aarch64.manylinux_2_28_aarch64.whl CPython 3.10 CPython 3.10 Linux glibc 2.28+ ARM64, Linux glibc 2.17+ ARM64 Details
lap-0.5.13-cp310-cp310-manylinux1_x86_64.manylinux_2_28_x86_64.manylinux_2_5_x86_64.whl CPython 3.10 CPython 3.10 Linux glibc 2.5+ x86-64, Linux glibc 2.28+ x86-64 Details
lap-0.5.13-cp310-cp310-macosx_11_0_arm64.whl CPython 3.10 CPython 3.10 macOS 11.0+ ARM64 Details
lap-0.5.13-cp310-cp310-macosx_10_9_x86_64.whl CPython 3.10 CPython 3.10 macOS 10.9+ x86-64 Details
lap-0.5.13-cp39-cp39-win_arm64.whl CPython 3.9 CPython 3.9 Windows ARM64 Details
lap-0.5.13-cp39-cp39-win_amd64.whl CPython 3.9 CPython 3.9 Windows x86-64 Details
lap-0.5.13-cp39-cp39-musllinux_1_2_x86_64.whl CPython 3.9 CPython 3.9 Linux musl 1.2+ x86-64 Details
lap-0.5.13-cp39-cp39-musllinux_1_2_aarch64.whl CPython 3.9 CPython 3.9 Linux musl 1.2+ ARM64 Details
lap-0.5.13-cp39-cp39-manylinux2014_aarch64.manylinux_2_17_aarch64.manylinux_2_28_aarch64.whl CPython 3.9 CPython 3.9 Linux glibc 2.17+ ARM64, Linux glibc 2.28+ ARM64 Details
lap-0.5.13-cp39-cp39-manylinux1_x86_64.manylinux_2_28_x86_64.manylinux_2_5_x86_64.whl CPython 3.9 CPython 3.9 Linux glibc 2.5+ x86-64, Linux glibc 2.28+ x86-64 Details
lap-0.5.13-cp39-cp39-macosx_11_0_arm64.whl CPython 3.9 CPython 3.9 macOS 11.0+ ARM64 Details
lap-0.5.13-cp39-cp39-macosx_10_9_x86_64.whl CPython 3.9 CPython 3.9 macOS 10.9+ x86-64 Details
lap-0.5.13-cp38-cp38-win_amd64.whl CPython 3.8 CPython 3.8 Windows x86-64 Details
lap-0.5.13-cp38-cp38-musllinux_1_2_x86_64.whl CPython 3.8 CPython 3.8 Linux musl 1.2+ x86-64 Details
lap-0.5.13-cp38-cp38-musllinux_1_2_aarch64.whl CPython 3.8 CPython 3.8 Linux musl 1.2+ ARM64 Details
lap-0.5.13-cp38-cp38-manylinux2014_aarch64.manylinux_2_17_aarch64.manylinux_2_28_aarch64.whl CPython 3.8 CPython 3.8 Linux glibc 2.28+ ARM64, Linux glibc 2.17+ ARM64 Details
lap-0.5.13-cp38-cp38-manylinux1_x86_64.manylinux_2_28_x86_64.manylinux_2_5_x86_64.whl CPython 3.8 CPython 3.8 Linux glibc 2.5+ x86-64, Linux glibc 2.28+ x86-64 Details
lap-0.5.13-cp38-cp38-macosx_11_0_arm64.whl CPython 3.8 CPython 3.8 macOS 11.0+ ARM64 Details
lap-0.5.13-cp38-cp38-macosx_10_9_x86_64.whl CPython 3.8 CPython 3.8 macOS 10.9+ x86-64 Details
lap-0.5.13-cp37-cp37m-win_amd64.whl CPython 3.7 CPython 3.7 pymalloc Windows x86-64 Details
lap-0.5.13-cp37-cp37m-musllinux_1_2_x86_64.whl CPython 3.7 CPython 3.7 pymalloc Linux musl 1.2+ x86-64 Details
lap-0.5.13-cp37-cp37m-musllinux_1_2_aarch64.whl CPython 3.7 CPython 3.7 pymalloc Linux musl 1.2+ ARM64 Details
lap-0.5.13-cp37-cp37m-manylinux_2_17_aarch64.manylinux2014_aarch64.whl CPython 3.7 CPython 3.7 pymalloc Linux glibc 2.17+ ARM64 Details
lap-0.5.13-cp37-cp37m-manylinux_2_5_x86_64.manylinux1_x86_64.manylinux_2_17_x86_64.manylinux2014_x86_64.whl CPython 3.7 CPython 3.7 pymalloc Linux glibc 2.17+ x86-64, Linux glibc 2.5+ x86-64 Details
lap-0.5.13-cp37-cp37m-macosx_10_9_x86_64.whl CPython 3.7 CPython 3.7 pymalloc macOS 10.9+ x86-64 Details

Total release size: 99.1 MB

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This release

0.5.13 This release

62 release files

0.4.0

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0.3.0

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