LAPJV: Solve linear assignment problem using LAPJV
Description
Use the algorithm of Jonker1987;textualTreeDist to solve the
Linear Sum Assignment Problem (LSAP).
Usage
LAPJV(x)
Value
LAPJV() returns a list with two entries: score, the score of the
optimal matching;
and matching, the columns matched to each row of the matrix in turn.
The Linear Assignment Problem seeks to match each row of a matrix with a
column, such that the cost of the matching is minimized.
The Jonker & Volgenant approach is a faster alternative to the Hungarian
algorithm Munkres1957TreeDist, which is implemented in
clue::solve_LSAP().
Note: the JV algorithm expects integers. In order to apply the function
to a non-integer n, as in the tree distance calculations in this package,
each n is multiplied by the largest available integer before applying
the JV algorithm. If two values of n exhibit a trivial difference --
e.g. due to floating point errors -- then this can lead to interminable
run times. (If numbers of the magnitude of billions differ only in their
last significant digit, then the JV algorithm may undergo billions of
iterations.) To avoid this, integers over 2^22 that differ by a value of
8 or less are treated as equal.
References
See Also
Implementations of the Hungarian algorithm exist in adagio,
RcppHungarian, and clue and lpSolve; for larger matrices,
these are substantially slower. (See discussion at Stack Overflow.)