Optimization of linear placements for wirelength minimization with free sites

We study a type of linear placement problem arising in detailed placement optimization of a given cell row in the presence of white-space (extra sites). In this single-row placement problem, the cell order is fixed within the row; all cells in other rows are also fixed. We give the first solutions to the single-row problem: (i) a dynamic programming technique with time complexity O(m/sup 2/) where m is the number of nets incident to cells in the given row, and (ii) an O(m log m) technique that exploits the convexity of the wirelength objective. We also propose an iterative heuristic for improving cell ordering within a row; this can be run optionally before applying either (i) or (ii). Experimental results show an average of 6.5% wirelength improvement on industry test cases when our methods are applied to the final output of a leading industry placement tool.