clue (version 0.3-27)

solve_LSAP: Solve Linear Sum Assignment Problem

Description

Solve the linear sum assignment problem using the Hungarian method.

Usage

solve_LSAP(x, maximum = FALSE)

Arguments

x

a matrix with nonnegative entries and at least as many columns as rows.

maximum

a logical indicating whether to minimize of maximize the sum of assigned costs.

Value

• An object of class "solve_LSAP" with the optimal assignment of rows to columns.

encoding

UTF-8

Details

If $nr$ and $nc$ are the numbers of rows and columns of x, solve_LSAP finds an optimal assignment of rows to columns, i.e., a one-to-one map p of the numbers from 1 to $nr$ to the numbers from 1 to $nc$ (a permutation of these numbers in case x is a square matrix) such that $\sum_{i=1}^{nr} x[i, p[i]]$ is minimized or maximized.

This assignment can be found using a linear program (and package lpSolve provides a function lp.assign for doing so), but typically more efficiently and provably in polynomial time $O(n^3)$ using primal-dual methods such as the so-called Hungarian method (see the references).

References

C. Papadimitriou and K. Steiglitz (1982), Combinatorial Optimization: Algorithms and Complexity. Englewood Cliffs: Prentice Hall.

Examples

x <- matrix(c(5, 1, 4, 3, 5, 2, 2, 4, 4), nr = 3)
solve_LSAP(x)
solve_LSAP(x, max = TRUE)