hungarian

IMPORTANT: The pathfinding crate has a significantly faster implementation of this algorithm (benchmarks below), uses traits to abstract over cost matrices, and is also better maintained. I recommend using it instead.

A simple Rust implementation of the Hungarian (or Kuhn–Munkres) algorithm. Should run in O(n^3) time and take O(m*n) space, given an m * n rectangular matrix (represented as a 1D slice).

Derived and modified from this great explanation.

Usage

Add the following to your Cargo.toml file:

[dependencies]
hungarian = "1.1.1"

Add the following to the top of your binary or library:

extern crate hungarian;

use hungarian::minimize;

And you should be good to go! For more information, check out the documentation.

Recent Changes

1.1.1
- Version bump so the pathfinding redirect appears on crates.io.
1.1.0
- Greatly optimized performance (by a factor of 2-4 on benchmarks on matrices from 5x5 to 100x100)
- Now uses num-trait to take generic integer weights
- Now backed by ndarray to scale better with larger inputs
1.0.0
- Greatly improved source code documentation
- Renamed hungarian function to minimize
- Now handle arbitrary rectangular matrices
- Added more test cases to cover non-square matrices
- Now returns Vec<Option<Usize>> to handle when not all columns are assigned to rows
0.1.0
- Initial release
- Working base algorithm, but only works for square matrices.
- Not well documented

Notes

Instead of using splitting logic across files and helper functions, I tried to simplify and condense the above explanation into a single, simple function while maintaining correctness. After trawling the web for test cases, I'm reasonably confident that my implementation works, even though the end result looks fairly different.

Please let me know if you find any bugs!

Performance

Benchmarks were obtained using Criterion.rs, with the following two types of cost matrices:

     Worst Case           |       Generic Case
                          |
   -------------          |       -------------
   | 1 | 2 | 3 | ...      |       | 1 | 2 | 3 |
   -------------          |       -------------
   | 2 | 4 | 6 | ...      |       | 4 | 5 | 6 |
   -------------          |       -------------
   | 3 | 6 | 9 | ...      |       | 7 | 8 | 9 |
   -------------          |       -------------
     .   .   .            |
     .   .   .            |
     .   .   .            |
                          |
C(i, j) = (i + 1)(j + 1)  |  C(i, j) = (i * width) + j

Criterion Results

Cost Matrix	Matrix Size	`hungarian` Average Runtime	`pathfinding` Average Runtime
Worst-Case	5 x 5	2.42 us	1.19 us
Worst-Case	10 x 10	20.38 us	4.24 us
Worst-Case	25 x 25	546.88 us	59.66 us
Worst-Case	50 x 50	6.97 ms	422.05 us
Generic	5 x 5	1.75 us	871.24 ns
Generic	10 x 10	7.49 us	3.50 us
Generic	25 x 25	86.33 us	33.91 us
Generic	50 x 50	556.48 us	285.69 us
Generic	100 x 100	3.97 ms	1.93 ms