# Matching Algorithms in R and C++

Computes matching algorithms quickly using Rcpp. Implements the Gale-Shapley Algorithm to compute the stable matching for two-sided markets, such as the stable marriage problem and the college-admissions problem. Implements Irving's Algorithm for the stable roommate problem. Implements the top trading cycle algorithm for the indivisible goods trading problem.

`matchingR` is an R package which quickly computes the Gale-Shapley algorithm, Irving's algorithm for the stable roommate problem, and the top trading cycle algorithm for large matching markets. The package provides functions to compute the solutions to the stable marriage problem, the college admission problem, the stable roommates problem, and the house allocation problem.

The package may be useful when the number of market participants is large or when many matchings need to be computed (e.g., for simulation or estimation purposes). It has been used in practice to compute the Gale-Shapley stable matching with 30,000 participants on each side of the market.

Matching markets are common in practice and widely studied by economists. Popular examples include

`matchingR` may be installed from CRAN:

``install.packages("matchingR")``

The latest development release is available from GitHub:

``devtools::install_github("jtilly/matchingR")``

Stable Marriage Problem

``# stable marriage problem with three men and two womenuM = matrix(c(1.0, 0.5, 0.0,              0.5, 0.0, 0.5), nrow = 2, ncol = 3, byrow = TRUE) uW = matrix(c(0.0, 1.0,              0.5, 0.0,              1.0, 0.5), nrow = 3, ncol = 2, byrow = TRUE) matching = galeShapley(uM, uW)matching\$engagements#>      [,1]#> [1,]    3#> [2,]    1matching\$single.proposers#> [1] 2galeShapley.checkStability(uM, uW, matching\$proposals, matching\$engagements)#> [1] TRUE``

``# college admissions problem with five students and two colleges with two slots eachset.seed(1)nstudents = 5ncolleges = 2uStudents = matrix(runif(nstudents*ncolleges), nrow=ncolleges, ncol=nstudents)uStudents#>           [,1]      [,2]      [,3]      [,4]       [,5]#> [1,] 0.2655087 0.5728534 0.2016819 0.9446753 0.62911404#> [2,] 0.3721239 0.9082078 0.8983897 0.6607978 0.06178627uColleges = matrix(runif(nstudents*ncolleges), nrow=nstudents, ncol=ncolleges)uColleges#>           [,1]      [,2]#> [1,] 0.2059746 0.4976992#> [2,] 0.1765568 0.7176185#> [3,] 0.6870228 0.9919061#> [4,] 0.3841037 0.3800352#> [5,] 0.7698414 0.7774452matching = galeShapley.collegeAdmissions(uStudents, uColleges, slots=2)matching\$matched.students#>      [,1]#> [1,]   NA#> [2,]    2#> [3,]    2#> [4,]    1#> [5,]    1matching\$matched.colleges#>      [,1] [,2]#> [1,]    5    4#> [2,]    3    2galeShapley.checkStability(uStudents, uColleges, matching\$matched.students, matching\$matched.colleges)#> [1] TRUE``
``# stable roommate problem with four students and two roomsset.seed(2)n = 4u = matrix(runif(n^2),  nrow = n, ncol = n)u#>           [,1]      [,2]      [,3]      [,4]#> [1,] 0.1848823 0.9438393 0.4680185 0.7605133#> [2,] 0.7023740 0.9434750 0.5499837 0.1808201#> [3,] 0.5733263 0.1291590 0.5526741 0.4052822#> [4,] 0.1680519 0.8334488 0.2388948 0.8535485results = roommate(utils = u)results#>      [,1]#> [1,]    2#> [2,]    1#> [3,]    4#> [4,]    3``
``# top trading cycle algorithm with four housesset.seed(2)n = 4u = matrix(runif(n^2),  nrow = n, ncol = n)u#>           [,1]      [,2]      [,3]      [,4]#> [1,] 0.1848823 0.9438393 0.4680185 0.7605133#> [2,] 0.7023740 0.9434750 0.5499837 0.1808201#> [3,] 0.5733263 0.1291590 0.5526741 0.4052822#> [4,] 0.1680519 0.8334488 0.2388948 0.8535485results = toptrading(utils = u)results#>      [,1]#> [1,]    2#> [2,]    1#> [3,]    3#> [4,]    4``

# matchingR 1.3

• Allow colleges to have different numbers of slots #31
• Change row names in vignette #34
• Remove need for microbenchmark package #35
• Registration of entry points in compiled code

# matchingR 1.2.2

This is a minor update.

• Colleges may have different numbers of slots in the college admissions problem (#30)

# matchingR 1.2.1

This is a minor update.

• Fixed bug in galeShapley.checkStability that resulted in UBSAN throwing an error

# matchingR 1.2

• Fixed a bug in the stable roommate matching algorithm that caused problems on Mac OS X / clang
• Changed function names throughout the package (deprecated old function names)
• Updated documentation
• Removed option to define preferences in row major order

# matchingR 1.1.1

This is a minor update.

• It fixes a memory leak warning in the stable roommate algorithm.
• It includes minor edits of the vignettes and documentation.
• We have substantially shortened the computational performance vignette so that the package can be built and checked faster

# matchingR 1.1

This is a major update that added additional algorithms to the package.

• Added algorithm to compute a solution to the stable roommate problem (`roommate`)
• Added top trading cycle algorithm (`toptrading`)
• Switched the layout of preference matrices from row order to column order to make the code faster
• Added two vignettes: An introductory vignette to the package in general and a computational performance vignette

# matchingR 1.0.1

Initial release that computes two versions of the Gale-Shapley algorithm:

• Stable Marriage Problem

# Reference manual

install.packages("matchingR")

1.3.3 by Jan Tilly, 8 months ago

https://github.com/jtilly/matchingR/

Report a bug at https://github.com/jtilly/matchingR/issues/

Browse source code at https://github.com/cran/matchingR

Authors: Jan Tilly , Nick Janetos

Documentation:   PDF Manual

Task views: Optimization and Mathematical Programming