Almost optimum placement legalization by minimum cost flow and dynamic programming

VLSI placement tools usually work in two steps: First, the cells that have to be placed are roughly spread out over the chip area ignoring disjointness (global placement). Then, in a second step, the cells are moved to their final position such that all overlaps are removed and all additional constraints are met (detailed placement or legalization). We consider algorithms for legalization. In particular, we analyze a generic legalization algorithm based on minimum cost flows and dynamic programming. Specializations are being used in industry for many years, and an improved version was proposed very recently in [2]. The objective of all these algorithms is to minimize the weighted sum of (squared) movements, i.e. they assume the placement to be already optimized except for not being legal. To evaluate results, we propose two different lower bounds for the legalization problem, one based on linear assignment, and the other one based on an integer linear programming relaxation. We prov...

• Type: Conference
• Year: 2004
• Where: ISPD
• Authors: Ulrich Brenner, Anna Pauli, Jens Vygen
• Keywords: Algorithm, Hardware, ISPD 2004, Legalization Problem, Lower Bound