A common cut mask is employed to define a gate pattern and a local interconnect pattern so that local interconnect structures and gate structures are formed with zero overlay variation relative to one another. A local interconnect structure may be laterally spaced from a gate structure in a first horizontal direction, and contact another gate structure in a second horizontal direction that is different from the first horizontal direction. Further, a gate structure may be formed to be collinear with a local interconnect structure that adjoins the gate structure. The local interconnect structures and the gate structures are formed by a common damascene processing step so that the top surfaces of the gate structures and the local interconnect structures are coplanar with each other.