Extending pitchmatching algorithms to layouts with multiple grid constraints

Pitchmatching algorithms are widely used in layout environments where no grid constraints are imposed. However, realistic layouts include multiple grid constraints which facilitate the applications of automatic routing. Hence, pitchmatching algorithms should be extended to those realistic layouts. The paper formulates a pitchmatching problem with multiple grid constraints. An algorithm for solving this problem is constructed by extending conventional pitchmatching algorithms. The computational complexity is also discussed in comparison with a conventional naive algorithm. Finally, examples and application results to realistic layouts are presented.