Noise analysis has been an important and difficult part of design flow of very large-scale integrated (VLSI) systems in many years. In this thesis, the problem of signal alignment resulting in possible maximum peak interconnect coupling noise and propose a variation aware technique for computing combined noise pulse taking into account timing constraints on signal transitions has been discussed. This work shows that the worst noise alignment algorithm can be formulated as mixed integer programming (MLIP) problem both in deterministic window cases and variational window cases. For deterministic window cases, it is assumed that timing windows are given for each aggressor inputs and the victim net is quite. It compares the results from proposed method with the most known and widely used method for computing the worst aggressor alignment - sweeping line algorithm, to verify its correctness and efficiency. For variation window cases, as variations of process and environmental parameters result in variation of start and end points of timing windows, linear approximation is used for approximating effect of process and environmental variations. One of the biggest advantages of MILP formulation of aggressor alignment problem has also been discussed, which is the ability to be easily extended to more complex cases such as non-triangle noise pulses, victim sensitivity window and discontinuous timing windows, this work shows that such extension can be solved by algorithm and does not require development of new algorithms. Therefore, this novel technique can handle noise alignment problem both in deterministic and variational cases and can be easily extended for more complex cases --Abstract, page iii
