# Assignment

Routines to solve the linear assignment problem, and the *k*-best assignment problem.

A variant of the Jonker-Volgenant algorithm is used to solve the linear assignment problem, this algorithm is in general faster than the Hungarian/Kuhn-Munkres algorithm. Murty's algorithm combined with the modified Jonker-Volgenant algorithm is used to solve the *k*-best assignment problem. Algorithms are described in detail in [1].

This is a Julia port of the Matlab code for solving the assignment problem from the TrackerComponentLibrary produced by D. F. Crouse [2], released into the public domain by the US Naval Research Laboratory.

This work is not affliated with or endorsed by the US Naval Research Laboratory.

### Examples

```
julia> using Assignment
julia> M=rand(1:100,3,4)
3×4 Matrix{Int64}:
77 51 42 67
72 53 47 4
24 50 77 96
julia> sol = find_best_assignment(M)
AssignmentSolution(CartesianIndex.(1:3, [3, 4, 1]), 70)
julia> sum(M[sol])
70
julia> max_sol = find_best_assignment(M', true)
AssignmentSolution(CartesianIndex.([1, 2, 4], 1:3), 226)
julia> sols = find_kbest_assigments(M, 5)
5-element Vector{Assignment.AssignmentSolution{Int64, Int64}}:
AssignmentSolution(CartesianIndex.(1:3, [3, 4, 1]), 70)
AssignmentSolution(CartesianIndex.(1:3, [2, 4, 1]), 79)
AssignmentSolution(CartesianIndex.(1:3, [3, 4, 2]), 96)
AssignmentSolution(CartesianIndex.(1:3, [3, 2, 1]), 119)
AssignmentSolution(CartesianIndex.(1:3, [2, 3, 1]), 122)
julia> max_sols = find_kbest_assignments(M, 5, true)
5-element Vector{Assignment.AssignmentSolution{Int64, Int64}}:
AssignmentSolution(CartesianIndex.(1:3, [1, 2, 4]), 226)
AssignmentSolution(CartesianIndex.(1:3, [1, 3, 4]), 220)
AssignmentSolution(CartesianIndex.(1:3, [2, 1, 4]), 219)
AssignmentSolution(CartesianIndex.(1:3, [4, 1, 3]), 216)
AssignmentSolution(CartesianIndex.(1:3, [3, 1, 4]), 210)
```

# References

[1] D. F. Crouse, "Advances in displaying uncertain estimates of multiple targets," in Proceedings of SPIE: Signal Processing, Sensor Fusion, and Target Recognition XXII, vol. 8745, Baltimore, MD, Apr. 2013. [2] D. F. Crouse, "The Tracker Component Library: Free Routines for Rapid Prototyping," IEEE Aerospace and Electronic Systems Magazine, vol. 32, no. 5, pp. 18-27, May. 2017