# LinearAssignment: Solve linear assignment problem In GraphAlignment: GraphAlignment

## Description

Solve the linear assignment problem specified by the cost matrix.

## Usage

 `1` ```LinearAssignment(matrix) ```

## Arguments

 `matrix` cost matrix

## Details

This function solves the linear assignment problem defined by the input matrix. [Jonker, Volgenant 1987]

## Value

The return value is a permutation vector equal to the solution of the linear assignment problem specified by the cost matrix. The result is the permutation P for which MP is minimal (where M is the cost matrix).

## Author(s)

Joern P. Meier, Michal Kolar, Ville Mustonen, Michael Laessig, and Johannes Berg

## References

Jonker, R & Volgenant, A. (1987) Computing 38, 325–340.

## Examples

 ```1 2 3``` ``` m <- matrix(rnorm(25), 5, 5) px <- LinearAssignment(round(-1000 * (m / max(abs(m))))) m[px,] ```

### Example output

```           [,1]       [,2]       [,3]       [,4]        [,5]
[1,]  1.9361372  0.4799021  1.2529215  0.0323784  0.06418556
[2,] -2.6065505  1.5668487 -0.7452492  0.0750315 -0.01817436
[3,]  0.1017669 -0.4144199 -0.2252630 -0.9694327 -0.37202021
[4,]  0.4829084 -1.6126931  0.4616213  0.7664048  0.28469562
[5,] -0.7961925 -0.1486903  0.3760055 -0.1566079  0.45359655
```

GraphAlignment documentation built on Nov. 8, 2020, 6:56 p.m.