---
bibliography: REFERENCES.bib
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# Carousel
*A simple Stable Matching solver.*

`carousel` is a solver for the 
[Envy-free](https://en.wikipedia.org/wiki/Envy-free_matching)
[Stable matching problem](https://en.wikipedia.org/wiki/Stable_marriage_problem) based on some naive modifications to the 
[Gale-Shapley Algorithm](https://en.wikipedia.org/wiki/Gale%E2%80%93Shapley_algorithm), written in Python.

## Algorithms

### Gale-Shapley Deferred Acceptance

- Gives a solution to the basic problem.

### GS + Rotation Enumeration of Solutions

- Can implement post-selection measures/constraints/criteria.

### Integer Programming (Huang++)

### Polytope Solution Sampling (Large Problems)

### Brute-Force Combinatoric Search
A benchmark/testbed implementation. Beware.

### More?
Contribute!

## Data - Input/Output
All [input table formats supported by `polars`](https://docs.pola.rs/user-guide/io/) are supported by `carousel` (`csv`, `excel`, `json` to name a few), 
which accepts a few inter-related tabular schemes for the input/output data.

### Input
Input describes the preferences/rankings of the "applicants" of "reviewers" to which they will be matched (possibly many-to-one, as in the "College Admission Problem"), as well as the preferences/rankings for the reviwers of applicants.
Input should be in one of two forms:

#### Preferences
Preferences enumerate by-name some preferences in descending order, 
e.g. the fruit preferences of Alice, Bob and Charlie are:

| Alice  | Bob    | Charlie |
|--------|--------|---------|
| apple  | banana | cherry  |
| cherry | apple  | banana  |
| banana | cherry | apple   |

where for e.g. Alice prefers apples to cherries (so they appear higher in her preferences).

#### Rankings
Rankings are like preferences, but are numerically ordered against a list of things;
e.g. Alice, Bob and Charlie rank the fruit apples, bananas and cherries as:

| fruit  | Alice | Bob | Charlie |
|--------|-------|-----|---------|
| apple  |   1   |  2  |    3    |
| banana |   3   |  1  |    2    |
| cherry |   2   |  3  |    1    |

### Intermediate

#### Ranking Matrix
In order to perform a matching, `carousel` either needs a pair of preferences
(e.g. a set of doctor's preferences for residencies, and a set of residencies' preferences for doctors),
a pair of corresponding rankings. A ranking matrix is a concise way to express
a pair of rankings - used to display rankings:

| names   | Alice      | Bob     | Charlie   |
|---------|------------|---------|-----------|
| Baylor  |   (1, 3)   |  (2, 2) |   (3, 1)  |
| CaseMed |   (3, 2)   |  (1, 1) |   (2, 3)  |
| Emory   |   (2, 1)   |  (3, 3) |   (1, 2)  |


#### Priorities
Internally, preferences/rankings are often serialized to rows as a priority listing of the form:

| App.  | Rank | Rev |
|-------|---|--------|
| Alice | 1 | apple  |
| Alice | 2 | cherry |
| Alice | 3 | banana |
| Bob 	| 1 | banana |
| Bob   | 2 | apple  |
| Bob   | 3 | cherry |
| Charlie | 1 | cherry |
| Charlie | 2 | banana |
| Charlie | 3 | apple  |

(in no specific row order). This is not a supported input format in the frontends, but may be relevant
when interacting with the package programmatically - priorities can be followed as edges in a graph.

### Output

#### Matching
A matching is a table whose rows list the applicants matched to each reviewer
e.g. a matching from the med-school ranking matrix in the previous section might look like

| Baylor | CaseMed | Emory   |
|--------|---------|---------|
| Alice  | Bob     | Charlie |
| `None` | Daina   | `None`  |

#### Assignments
An assignment is a table whose row lists which reviewer each applicant was matched to.
e.g.

| Alice  | Bob     | Charlie | Daina   |
|--------|---------|---------|---------|
| Baylor | CaseMed | Emory   | CaseMed |

TODO check/make stable.

TODO matching more people per school e.g.




## Usage

There are 4 main ways to use Carousel:

### UO Pages Server - CGI Form
An HTML form submission interface is hosted at

> [`https://pages.uoregon.edu/tgorordo/forms/carousel.html`](https://pages.uoregon.edu/tgorordo/forms/carousel.html)

using the [pages.uoregon.edu CGI feature](https://service.uoregon.edu/TDClient/2030/Portal/KB/ArticleDet?ID=43069).

Submit your applicant and reviewer preferences in tabular form,
or as excel uploads and the server will return a table of matches for you to choose from.

This resource has *very* limited compute, so excessive usage might result in limitations or restricted access.
Try not to ruin a good thing! A moderate number of problems on the scale of those in the Examples section below should be sustainable.

### Command Line Binary

TODO

### GUI Binary

TODO

### Python Library/Development
If you prefer to invoke `carousel` directly (or incorporate it as a library into another script)
in a python environment instead of using any of the bundled/released versions of the program described above (or wish to
reproduce those bundles), you can do so using the [`uv` environment/package/project manager](https://github.com/astral-sh/uv)
or a raw python virtual environment using the [`venv` module](https://docs.python.org/3/library/venv.html)
(if you need an intro to python `venv`s see [this page](https://pages.uoregon.edu/tgorordo/uoph410-510a_Image-Analysis/venvs.html)).

Some extra command-line development conveniences are available if you use the tools:  

- [`just`](https://github.com/casey/just) is a taskrunner that can execute the provided `justfile` of some common useful commands.
- [`direnv`](https://github.com/direnv/direnv) with [`nix` (shell)](https://github.com/NixOS/nix) can guarantee minimal development tooling without polluting your broader environment. i.e. they can auto-install and run all of carousel's tooling in an environment specific to your development directory.

but everything provided by these tools can also be done using more standard/default shell tooling. 
[`uv`](https://github.com/astral-sh/uv) as your package/environment manager is highly recommended, however.

TODO

## Post-Selection
It's often desirable to enforce additional criteria on solutions 
that are not well-posed within the core optimization problem.
Since the solver itself is stochastic to some extent, these are often most easily implemented 
by a post-selection on a sampling of solutions.


## Examples
Here are some usage examples:

### University of Oregon Physics Department Graduate TA Assignments
TODO

### Caltech Housing Rotation
TODO

## References
*See [`REFERENCES.bib`](REFERENCES.bib)*

[1]: 

TODO