$r^{\ast}$ gets its minimum value, $$\label{rmin}
r^{\ast}(r_h) = r_{min} \simeq -\infty.$$

According to the proposal of [@Brown:2015lvg], the complexity of dual theory is given by the gravitational action evaluated on a region of spacetime known as the WDW patch. The WDW patch is given by the union of all the spatial slices anchored at a given boundary time [@Susskind:2014rva]. Here we use this definition and impose it in the flat space. In the flat space, as it was shown in figure 1, the WDW patch is the intersection of spatial slices anchored at future or null infinity. It is clear that the WDW patch in the flat scenario connects to the infinity via the null geodesics and does not reach it. A similar situation happens in the holographic description of the BMSFT entanglement entropy where the minimal surface does not reach the boundary and connects to it via two null geodesics [@Jiang:2017ecm]. Thus our prescription is a natural extension of the WDW patch definition and also is consistent with the holographic description of the entanglement entropy in flat spacetimes.

In this paper we consider asymptotically flat geometries which are given by taking the flat space limit from the asymptotically AdS 