Logical vectors pairing maximization

Question

I have a DF of logical vectors as follows:

DF <- data.frame(c(T,T,F), c(T,F,T), c(F,T,F))

I want to find row-column pairs under the condition that the combination has a TRUE value.

So, DF[1,2] represents a possible pair, but DF[2,2] does not.

Once in pair, the row and the column are excluded to make new pairs.

Depending on the data-set, there with be different pairing possibilities. It may also be impossible to find a pair for all the rows or columns.

My question is: What kind of algorithm/library can I use to maximize the quantity of pairs?

In the example given, the pairing solution would be this one:

DF[3,2]
DF[2,3]
DF[1,1]

Answer 1

This is the maximum matching problem of a bipartite graph formed by the rows and columns connected according to the matrix DF. There are a few packages you can use for this problem. One option is the RcppHungarian package, with HungarianSolver.

DF <- data.frame(c(T,T,F), c(T,F,T), c(F,T,F))

RcppHungarian::HungarianSolver(!DF)$pairs
#>      [,1] [,2]
#> [1,]    1    1
#> [2,]    2    3
#> [3,]    3    2

Answer 2

Not exactly sure about your logic, but maybe you want

which(as.matrix(DF), arr.ind=TRUE)
#      row col
# [1,]   1   1
# [2,]   2   1
# [3,]   1   2
# [4,]   3   2
# [5,]   2   3