We study several kinds of matching problems between two point processes. First we consider the set of integers $\\mathbb{Z}$. We assign a color red or blue with probability 1/2 to each integer. We match each red integer to a blue integer using some algorithm and analyze the matched edge length of the integer zero. Next we go to $\\mathbb{R}^{d}$. We consider matching between two different point processes and analyze a typical matched edge length $X$. There we see that the results vary significantly in different dimensions. In dimensions one and two (d=1,2), even $E[X^{d/2}]$ does not exist. On the other hand in dimensions more than two (d>2), $E[\\exp(cX^{d})]$ exist, where $c$ is a constant depends on $d$ only.