Analytical Minimization of Half - Perimeter
نویسنده
چکیده
Global placement of hypergraphs is critical in the top-down placement of large timing-driven designs 10, 16]. Placement quality is evaluated in terms of the half-perimeter wirelength (HPWL) of hyperedges in the original circuit hypergraph provided timing constraints are met. Analytical placers are instrumental in handling non-linear timing models 9, 3], but have two important drawbacks: (a) corresponding optimization algorithms are typically slower than top-down methods driven by multi-level mincut partitioning 2], and (b) hyperedges must be represented with net models 10, 17, 15, 8, 21, 20] which imply a mismatch of objective functions, with the alternative of computationally expensive linear programming (LP) 25, 16]. By comparing to optimal solutions produced by linear programming, we show that net models lead to solution quality loss. To address this problem, we present the rst analytical algorithm that does not require net models and permits a direct inclusion of non-linear delay terms 3]; this allows to avoid expensive linearization of delay terms in 16]. Our numerical engine utilizes well-known quadratically con-vergent Newton-type methods 5, 11] for speed; it produces solutions within 12% of the LP optimum. Empirical results are for industrial placement instances.
منابع مشابه
Analytical Placement of Hypergraphs | I
G lobal placement of hypergraphs is critical to modern physical implementation methodology for large timingdriven designs. Placement results are typically evaluated in terms of the half-perimeter wirelengths of hyperedges in the original circuit hypergraph. However, existing analytical placers rely on a heuristic transformation into a graph to enable classical linear and quadratic edgelength mi...
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