13.4 Force Directed Mongrel with Physical Net Constraints z Sung-Woo Hur Tung Cao Karthik Rajagopal Yegna Parasuram Bill Halpin Donga University Amit Chowdhary Vladimir Tiourin Syracuse Univ. Intel Corporation Intel Corporation and zyx ABSTRACT zyxwvutsr This paper describes a new force directed global placement algorithm that exploits and extends techniques from zyxwvut two leading placers, Force-directed [12] [26] and Mongrel [22]. It combines the strengths of force directed global placement with Mongrel’s cell congestion removal to significantly improve the quality of placement during the difficult overlap removal stage of global placement. This is accomplished by using the spreading force in [12] to direct and control Mongrel’s ripple move optimization. This new placer is called Force Directed Mongrel (FD-Mongrel). FD-Mongrel also incorporates physical net constraints [26], and improves the congestion model for sparse placements. We propose a new placement flow that uses a limited number of the spreading iterations of [12] to form a preliminary global placement. We then use the new FD-Mongrel described in this paper to remove cell overlaps, while meeting net constraints and optimizing wirelength. We present results on wirelength as well as timing driven placement flows. Categories and Subject Descriptors B.7.2 [Hardware, Integrated Circuits, Design Aids]: placement and routing General Terms Keywords Algorithms, Design. Timing Driven Placement, Force Directed Placement, Net Constraints,Mongrel 1. INTRODUCTION Automated cell placement has always been an important step in the fast and efficient design of VLSI circuits. Cell placement has a big impact on the key design parameters - wirelength, performance and routability of the design. With ongoing advances in the semiconductor process, circuit performance is becoming more dependent on the wire delays since wire delays do not reduce as rapidly as gate delays [4] [17]. Thus, there is a greater need to design efficient timing-driven placement algorithms for high speed interconnect dominated designs. Furthermore, the scaling down of semiconductor process allows larger designs and Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. DAC ’03, June 2-6,2003, Anaheim, Califomia,USA Copyright 2003 ACM 1-58113-688-9/03/0006 ... zyxwvuts $5.00. the importance of the placement step grows with design size [25]. Automated cell placement has been the subject of much research [1][2][7-12][14-16][19-261. One of the most powerful techniques for cell placement is the force-directed method for global placement by Eisenmann [ 121, called Kraftwerk. Kraftwerk uses forces derived from the cell congestion to remove cell overlaps during placement. The main advantage of the force-directed method is that it is an iterative approach that models the wirelength, cell congestion and timing in the same mathematical formulation. This allows smooth and simultaneous optimization of design in terms of these three parameters. Wire length and cell congestion are modeled as forces, while timing is modeled as higher net weights on timing-critical nets [12]. The forces for wirelength and cell congestion should be precisely weighted to result in an optimized design with little or no congestion. The weight on the spreading force which models cell congestion is initially small compared to the wirelength force, but is increased with every iteration to spread out the cells. Timing driven Kraftwerk has been recently improved by a more precise modeling of timing in KraftwerkNC [26]. KraftwerkNC models timing in terms of net constraints. A net constraint is an upper bound on the half-perimeter of the smallest rectangle that encloses all the nets’ connections. Net constraints are set on the critical nets by analyzing the timing of the design. KraftwerkNC generates good global placements with optimized wirelength and timing, but it does have a few drawbacks. KraftwerlcNC is very sensitive to the rate of increase of weight on the spreading force. If the weight on spreading force is increased rapidly, then the placement converges faster at the expense of wire length and timing. Therefore, the weight on spreading forces is increased slowly with every iteration. After the initial spreading of KraftwerkNC, there is little cell movement due to the equilibrium between the weight on spreading force and the wirelength force, even though there is localized congestion across the design. KraftwerkNC will ultimately remove most of the congestion by increasing the contribution of the spreading force at the potential cost of wirelength, timing and long runtimes. Also, the modeling of spreading forces on the cells on the boundary of the design is not accurate, which might lead to congestion on the boundary. The mathematical formulation in KraftwerkNC represents a net as a clique, which is a collection of edges connecting every cell pair in the net. Thus, the net length is not modeled accurately in terms of the half-perimeter of the bounding box of all cells connected to the net. This deficiency has more impact during the later Kraftwerk iterations. Mongrel [22], in contrast, is a set of hybrid techniques for cell placement. It starts by assigning cells to global bins in a grid imposed over the placement area. It then extracts a sub-circuit from the circuit, assigns new positions to the cells in the sub- 214