Abstract: Roughly described, a system enables quick and accurate depiction to a user of multi-patterning layout violations so that they may be corrected manually and in real time, and without interfering with normal manual editing process. In one embodiment, the system involves iteratively building tree structures with nodes identifying islands and arcs identifying multi-patterning spacing violations between the connected islands. The system detects coloring violations during the building of these tree structures, using the relationships previously inserted. The coloring violations preferably are reported to a user in the form of visual indications of the cycles among the candidate spacing violations, with the candidate spacing violations also themselves indicated visually and individually. The user can see intuitively how to move the islands around, and in which directions and by what distance, in order to remove a multi-patterning spacing violation and thereby break the cycle.

Abstract: Roughly described, a system enables quick and accurate depiction to a user of multi-patterning layout violations so that they may be corrected manually and in real time, and without interfering with normal manual editing process. In one embodiment, the system involves iteratively building tree structures with nodes identifying islands and arcs identifying multi-patterning spacing violations between the connected islands. The system detects coloring violations during the building of these tree structures, using the relationships previously inserted. The coloring violations preferably are reported to a user in the form of visual indications of the cycles among the candidate spacing violations, with the candidate spacing violations also themselves indicated visually and individually. The user can see intuitively how to move the islands around, and in which directions and by what distance, in order to remove a multi-patterning spacing violation and thereby break the cycle.

Abstract: An actuator control loop for controlling head position in a rotating media data storage system. The invention applies the compensation zero to the PES prior to summing it with the integrator. This scheme reduces transients caused by the integrator initialization step because the zero does not "see" the integrator initialization step. Transients that can result from coupling the integrator initialization to the zero can cause overshoot and ringing in the actuator, increasing settling time and reducing system performance. The present invention also provides a first sample velocity compensation scheme that removes the velocity correction factor from the PES signal in the first sample after a seek. This significantly reduces settling time and improves system performance. In one embodiment, the microprocessor of the present invention calculates a velocity compensation factor based on the PES signal. This signal is then superimposed on the integrator output.