Some Generalizations of the Euclidean Two-Sample Matching Problem
J. E. Yukich · Birkhäuser Boston eBooks · 1992
Let X 1, …,X n , Y 1,…, Y n be i.i.d with the uniform distribution λ on the unit square. The two-sample Euclidean matching problem, also called the transportation cost problem, involves the study of the functional $$T_{p}(n):=_{\pi}^ f (\frac{1}{n}\sum_{i=1}^{n}||X_{i}-Y_{\pi(i)}||^{p})^{1/p},$$ where π runs over all permutations of the first n integers and ∥ ∥ denotes the Euclidean norm.