Rectangular Linear Assignment Problem - Jonker-Volgenant Solver (rlapjv)

About

This is a fork of lapjv project (https://github.com/src-d/lapjv) to extend JV solver to rectangular matrix (2d numpy array). Instead of transforming the rectangular matrix to a square matrix, the rlapjv is to extend the lapjv algorithm in the algorithmic level (rlap.h). Thanks to AVX accelaration (credit to the original lapjv), the rlapjv is incredibly efficient. The square-to-rectangular extension is based on the paper:

Bijsterbosch, J. & Volgenant, A. Solving the Rectangular assignment problem and applications. Ann Oper Res (2010) 181: 443 https://doi.org/10.1007/s10479-010-0757-3.

Compared with the lapjv solver, two first initialization steps in lapjv are discarded, since the dual variables $v$ (price) are no longer unbounded ($v$ is less than or equal to zero). In this paper, several enhancements are described, but this package does not implement any but is a simple extension directly from lapjv. The enhancement will be the to-dos as well as the $k$-cardinality derivative of linear assignment problem.

Installation and Usage

Virtual environment is recommended for this dev python package. Here is an example of installation based on conda environment.

$ conda create --name rlap
$ source activate rlap
$ python setup.py install

To use the rlap is similar to lapjv. Here is a simple example.

import numpy as np
from rlapjv import rlapjv
dim0, dim1 = 800, 1000
costs = np.random.rand(dim0, dim1)
rind, cind, sumcost, u_price, v_price = rlapjv(costs)

To-Do

1. $\beta$-best enhancement in augmenting row reduction initialization
2. heap-based todo split enhancement in shortest augmenting path
3. algorithmic $k$-cardinality extension based on transformation