Graph based phase shift lithography mapping method and apparatus

For phase-shifting micro lithography, a method of assigning phase to a set of shifter polygons in a mask layer separated by a set of target features includes assigning a first phase to a first shifter polygon, identifying a set of target features that touch the first shifter polygon, and assigning a second phase to all shifter polygons in the set that touch the set of target features in contact with the first shifter polygon. The set of shifter polygons and the set of target features are separated into aggregates that are spatially isolated from each other such that the phase assignment in one aggregate does not affect the phase assignments in other aggregates. In one embodiment, the first shifter polygon in each aggregate is selected by merging the set of shifter polygons and set of target features into a large polygon, marking a vertex of the large polygon, checking the vertex to make sure it only touches one shifter polygon, and selecting the single shifter polygon touching the vertex as the first shifter polygon.