In the definition of this problem, the weight/cost function generally takes value in $\mathbb{Z}$ (or sometimes $\mathbb{Q}$). This is what I observed from some books (e.g. "Combinatorial Optimization: Polyhedra and Efficiency" by Alexander Schrijver) and some implementations I found on the web.

My question is: How does a real-valued cost function affect the solution, such as the Hungarian method?

Thank you in advance.

An Algorithmic Theory of Numbers, Graphs and Convexity. $\endgroup$ – Tony Huynh Nov 9 '15 at 14:26