On implementing 2D rectangular assignment algorithms

This paper reviews research into solving the two-dimensional (2D) rectangular assignment problem and combines the best methods to implement a k-best 2D rectangular assignment algorithm with bounded runtime. This paper condenses numerous results as an understanding of the "best" algorithm, a strong polynomial-time algorithm with a low polynomial order (a shortest augmenting path approach), would require assimilating information from many separate papers, each making a small contribution. 2D rectangular assignment Matlab code is provided.