Wirelength Estimation Research Articles

PROS 2.0: A Plug-In for Routability Optimization and Routed Wirelength Estimation Using Deep Learning

Recently, the topic of how to utilize prior knowledge obtained by machine-learning (ML) techniques during the EDA flow has been widely studied. In this article, we study this topic and propose a practical plug-in named PROS for both routability optimization and routed wirelength estimation which can be applied in the state-of-the-art commercial EDA tool or an academic EDA flow with negligible runtime overhead. PROS consists of three parts: 1) an effective fully convolutional network (FCN)-based predictor that only utilizes the data from placement result to forecast global routing (GR) congestion; 2) a parameter optimizer that can reasonably adjust GR cost parameters based on the prediction result to generate a better GR solution for detailed routing (DR); and 3) a convolutional neural network (CNN)-based wirelength estimator which can report accurate routed wirelength at the placement stage by using the predicted GR congestion. Experiments show that on the industrial benchmark suite in the advanced technology node, PROS can achieve high accuracy of GR congestion prediction and significantly reduce design rule checking (DRC) violations by 11.65% on average, and on the DAC-2012 benchmark suite, PROS can achieve a very low error rate (1.82%) for wirelength estimation which greatly outperforms that of FLUTE (21.52%) by 19.70%.

Power and performance analysis of 3D network-on-chip architectures

Emerging 3D integrated circuits(ICs) employ 3D network-on-chip(NoC) to improve power, performance, and scalability. The NoC Simulator uses the microarchitecture parameters to estimate the power and performance of the NoC. We explore the design space for 3D Mesh and Butterfly Fat Tree(BFT) NoC architecture using floorplan drive wire length and link delay estimation. The delay and power models are extended using Through Silicon Via (TSV) power and delay models. Serialization is employed to reduce the TSV area cost. Buffer space is equalised for a fair comparison between topologies. The Performance, Flits per Joules(FpJ) and Energy Delay Product(EDP) of six 2D and 3D variants of Mesh and BFT topologies (two and four layers) are analyzed by injecting synthetic traffic patterns. The 3D-4L Mesh exhibit better performance, energy efficiency (up to 4.5 × ), and EDP (up to 98 %) compared to other variants. This is because the overall length of the horizontal link is short and the number of TSVs is large (3 × ).

Optimization of thermal aware multilevel routing for 3D IC

Due to the technological advancements, the three dimensional Integrated Circuits become the most popular technology. But it has the major drawback of increased time consumption as well power consumption. This happens because of the increased wire length and routing path for connecting the components in chip. Thus it is essential to reduce the wire length for the purpose of enhancing the circuit speed and minimize the power dissipation. But there may be a chance of temperature rise due to the heat generated by the slacked layers which also needs to be reduced. Several traditional approaches have addressed the issues of temperature rise and layer assignment. But the utilization of through-silicon-via is considered. Thus a new stochastic based genetic algorithm is proposed in this work for reducing the thermal estimations. Also the length of wire can be reduced by determining the minimal path so as to connect the components. Both partitioning and routing process takes place in this approach. The performance of the proposed approach is analyzed using ISPD2008 dataset. Also the results of this stochastic based model are compared with the existing algorithm. The superiority of this proposed approach is proved with reduced wire length and temperature estimations.

Rectilinear Steiner Tree Construction Techniques Using PB-SAT-Based Methodology

Rectilinear Steiner Tree (RST) construction is a fundamental problem in very large scale integration (VLSI) physical design. Its applications include placement and routing in VLSI physical design automation (PDA) where wire length and timing estimations for signal nets are obtained. In this paper, a pseudo-Boolean satisfiability (PB-SAT)-based approach is presented to solve rectilinear Steiner tree problem. But large nets are a bottleneck for any SAT-based approach. Hence, to deal with large nets, a region-partitioning-based algorithm is taken into consideration, which eventually achieves a reasonable running time. Furthermore, a clustering-based approach is also explored to improve the partitioning of nets by identifying clusters and then applying a heuristic-based approach to get the minimum wire length for each set of the clusters. Experimental results obtained by these techniques show that the proposed algorithm can solve the RST problem very effectively even on large circuits and it outperforms the widely used RST algorithm FLUTE with 3[Formula: see text][Formula: see text][Formula: see text]to 9[Formula: see text][Formula: see text][Formula: see text]speedups.

A Study on Applying Parallelism for Construction of Steiner Tree Algorithms in VLSI Design

e present a survey of the different approaches that can be parallelized and also the parallel algorithms available today with special concern to Rectilinear steiner tree for VLSI Design and their appropriateness for high-performance computing. Thus, we review the parallel algorithms for solving the Stiener tree problem as it is of great importance for very large scale integration routing and wire length estimation. As the steiner problem in general is NP-hard, it is difficult to develop a polynomial-time algorithm to solve the problem exactly. This is why the most of research has looked at finding efficient heuristic algorithms. Additionally, many authors focused their work on utilizing the ever-increasing computational power and developed many parallel methods for solving the problem. Hence we are able to obtain better results in less time than ever before.The study shows that the accessibility of multi-core CPUs has given new impulse to the shared memory parallel programming approach., Hybrid parallel programming is the current way of harnessing the capabilities of computer clusters with multi-core nodes. On the other hand, high performance heterogeneous programming is found to be an increasingly well accepted paradigm, as a result of the availability of multi-core CPUs and GPUs systems. The use of open industry standards like OpenMP, MPI, or OpenCL, as opposed to proprietary solutions, seems to be the way to categorize and extend the use of parallel programming models. Here, we present a survey of the parallel methods for solving the stiener tree problem specifically for VLSI design

NCTU-GR: Efficient Simulated Evolution-Based Rerouting and Congestion-Relaxed Layer Assignment on 3-D Global Routing

The increasing complexity of interconnection designs has enhanced the importance of research into global routing when seeking high-routability (low overflow) results or rapid search paths that report wirelength estimations to a placer. This work presents two routing techniques, namely circular fixed-ordering monotonic routing and evolution-based rip-up and rerouting using a two-stage cost function in a high-performance congestion-driven 2-D global router. We also propose two efficient via-minimization methods, namely congestion relaxation by layer shifting and rip-up and reassignment, for a dynamic programming-based layer assignment. Experimental results demonstrate that our router achieves performance similar to the first two winning routers in ISPD 2008 Routing Contest in terms of both routability and wirelength at a 1.05 × and 18.47 × faster routing speed. Moreover, the proposed layer assignment achieves fewer vias and shorter wirelength than congestion-constrained layer assignment (COLA).

Through-Silicon Via Planning in 3-D Floorplanning

In this paper, we will study floorplanning in 3-D integrated circuits (3D-ICs). Although literature is abundant on 3D-IC floorplanning, none of them consider the areas and positions of signal through-silicon vias (TSVs). In previous research, signal TSVs are viewed as points during the floorplanning stage. Ignoring the areas, positions and connections of signal TSVs, previous research estimates wirelength by measuring the half-perimeter wirelength of pins in a net only. Experimental results reveal that 29.7% of nets possess signal TSVs that cannot be put into the white space within the bounding boxes of pins. Moreover, the total wirelength is underestimated by 26.8% without considering the positions of signal TSVs. The considerable error in wirelength estimation severely degrades the optimality of the floorplan result. Therefore, in this paper, we will propose a two-stage 3-D fixed-outline floorplaning algorithm. Stage one simultaneously plans hard macros and TSV-blocks for wirelength reduction. Stage two improves the wirelength by reassigning signal TSVs. Experimental results show that stage one outperforms a post-processing TSV planning algorithm in successful rate by 57%. Compared to the post-processing TSV planning algorithm, the average wirelength of our result is shorter by 22.3%. In addition, stage two further reduces the wirelength by 3.45% without any area overhead.

Layout Aware Optimization of High Speed Fixed Coefficient FIR Filters for FPGAs

We present a method for implementing high speed finite impulse response (FIR) filters on field programmable gate arrays (FPGAs). Our algorithm is a multiplierless technique where fixed coefficient multipliers are replaced with a series of add and shift operations. The first phase of our algorithm uses registered adders and hardwired shifts. Here, a modified common subexpression elimination (CSE) algorithm reduces the number of adders while maintaining performance. The second phase optimizes routing delay using prelayout wire length estimation techniques to improve the final placed and routed design. The optimization target platforms are Xilinx Virtex FPGA devices where we compare the implementation results with those produced by Xilinx Coregen, which is based on distributed arithmetic (DA). We observed up to 50% reduction in the number of slices and up to 75% reduction in the number of look up tables (LUTs) for fully parallel implementations compared to DA method. Also, there is 50% reduction in the total dynamic power consumption of the filters. Our designs perform up to 27% faster than the multiply accumulate (MAC) filters implemented by Xilinx Coregen tool using DSP blocks. For placement, there is a saving up to 20% in number of routing channels. This results in lower congestion and up to 8% reduction in average wirelength.

Near-linear wirelength estimation for FPGA placement

With rapid advances in integrated circuit technology, wirelength has become one of the most critical and important metrics in all phases of VLSI physical design automation, especially circuit placement. As the precise wirelength for a given placement can only be known after routing, accurate and fast-to-compute wirelength estimates are required by FPGA placement algorithms. In this paper, a new model, called star+, is presented for estimating wirelength during FPGA placement. The proposed model is continuously differentiable and can be used with both analytic and iterative-improvement placement methods. Moreover, the time required to calculate incremental changes in cost incurred by moving/swapping blocks can always be computed in O(1) time. Results show that when incorporated into the well-known VPR framework and tested using the 20 MCNC benchmarks, the star+ model achieves a 6-9% reduction in critical-path delay compared with the half-perimeter wirelength (HPWL) model, while requiring roughly the same amount of computational effort.

Hierarchical 3-D Floorplanning Algorithm for Wirelength Optimization

Three-dimensional (3-D) IC physical design problems are usually of higher complexity, with a greatly enlarged solution space due to multiple device structure. In this paper, a new 3-D floorplanning algorithm is proposed for wirelength optimization. Our main contributions and results can be summarized as follows. First, a new hierarchical flow of 3-D floorplanning with a new inter-layer partitioning method. The blocks are partitioned into different layers before floorplanning. A simulated annealing (SA) engine is used to partition blocks with the objective of minimizing the statistical wirelength estimation results. The solution quality is not degraded by the hierarchical flow. Second, floorplans of all the layers are generated in a SA process. Original 3-D floorplanning problem is transformed into solving several 2-D floorplanning problems simultaneously. The solution space is scaled down to maintain a low design complexity. Finally, Experimental results show that our algorithm improves wirelength by 14%-51% compared with previous 3-D floorplanning algorithms. The hierarchical approach is proven to be very efficient and offers a potential way for high-performance 3-D design

APWL-Y: An accurate and efficient wirelength estimation technique for hexagon/triangle placement

The Y architecture has recently received much attention due to its many potential advantages, such as substantially reduced wirelength, power consumption and significantly improved throughput. To fully utilize the virtues of Y architecture, several hexagon/triangle placement (HTP) algorithms suitable for the Y architecture were presented, however the wirelength optimization is not included in the algorithms. Wirelength estimation is fundamental to guide the wirelength optimization process in early design stages. In this paper, we present an accurate and efficient wirelength estimation technique called APWL-Y appropriate for the Y architecture, and especially for HTP floorplanner and placer. The average error of APWL-Y is 4.41% for 1.57 million nets from industrial circuits. When developing APWL-Y, we find out that 3-SMT wirelength is a power function of aspect ratio of bounding box of the given n-pin nets. The time complexity of APWL-Y is O ( n ) . APWL-Y is very effective to guide the wirelength optimization in a HTP placer. Moreover, we develop an efficient HTP algorithm with wirelength optimization driven by APWL-Y estimator. The placement results by our placer subject to different optimization objectives are presented. Compared to the HTP placer with only area optimization, our placer can reduce the wirelength by 54.3% with a small area overhead of 9.07% on average. In addition, we explore the HPWL technique in the Y architecture. To the best of our knowledge, this paper is the first in-depth study on wirelength estimation technique in Y architecture and HTP floorplanning optimization with consideration of interconnects.

A statistical methodology for wire-length prediction

In this paper, the classic wire-length estimation problem is addressed and a new statistical wire-length estimation approach that captures the probability distribution function of net lengths after placement and before routing is proposed. These types of models are highly instrumental in formalizing a complete and consistent probabilistic approach to design automation and design closure where, along with optimizing the pertinent cost function, the associated prediction error is also considered. The wire-length prediction model was developed using a combination of parametric and nonparametric statistical techniques. The model predicts not only the length of the net using input parameters extracted from the floorplan of a design, but also probability distributions that a net with given characteristics after placement will have a particular length. The model is validated using the learn-and-test and resubstitution techniques. The model can be used for a variety of purposes, including the generation of a large number of statistically sound, and therefore realistic, instances of designs. The net models were applied to the probabilistic buffer-insertion problem and substantial improvement was obtained in net delay after routing (~ 20%) when compared to a traditional bounding box (BBOX)-based buffer-insertion strategy

A priori wirelength and interconnect estimation based on circuit characteristics

Interconnect prediction is very important for early feasibility studies in modern design flows. Most of the current interconnect estimation techniques estimate either the average or the total wirelength and some qualitative measure of routing demand for circuits. A priori techniques estimate these parameters without actually performing circuit placement. We propose a new a priori interconnect and wirelength estimation methodology for island style field programmable gate arrays (FPGAs). For a given design, we estimate bounding box semiperimeter wirelengths of all nets for an optimized placement and the minimum number of tracks per channel required for successful routing on an FPGA device. We analyze the structural characteristics of circuits and limitations posed by the FPGA architecture to derive a consistent model for wirelength and routing demand estimation. We identify reconvergences present in a circuit as an important global circuit characteristic in wirelength prediction. Our overall results show that we have an average error of 11.6% w.r.t. semiperimeter wirelength measured from the optimized layout using VPR. Also, the number of routing tracks per channel is predicted with an average error of 13.2% of the detailed routing results from VPR.

Assessment of on-chip wire-length distribution models

Ultralarge-scale integrated (ULSI) chip design data is needed for an assessment of existing on-chip wirelength distribution models. Data extracted from modern chips such as high-performance microprocessors provide information about actual wire length requirements in ULSI chip designs. These requirements are compared with wirelength estimates obtained by evaluating existing models as functions of Rent's parameters that are extracted from the designs. This brief assesses the extent to which existing models estimate wirelength requirements in 100 ASIC-like control logic designs in the 1.3-GHz POWER4 microprocessor. For each design, physical design characteristics and wirelength requirements are measured and compared with model estimates. Lack of agreement between the data and models is observed for most designs, and possible reasons for the lack of agreement are discussed.

Toward the accurate prediction of placement wire length distributions in VLSI circuits

Since its introduction, Donath's technique for predicting placement wire length distributions has become one of the most popular techniques for a priori wire length estimation. However, in its original form, it was heavily constrained by the underlying circuit and architecture models. In this paper, we show how a careful relaxation of those constraints results in very high correlations between predicted and experimentally measured average wire lengths as well as, a much improved accuracy in predicting wire length distributions. Because the availability of the Rent characteristic is crucial for the quality of our model, we investigate how the prediction quality degrades when only an estimated characteristic is available. Such an estimation can be required to save computation time or when the complete netlist is not yet available (partial use of typical values). It turns out that a fitted /spl beta/-model, based on only a few partitioning levels, can still result in a relatively high-prediction quality. In particular, with respect to the wire length distribution, the results are considerably better than when Rent's Rule is used.

A priori wire length distribution models with multiterminal nets

Interconnections are quickly becoming a dominant factor in the design of computer chips. Techniques to estimate interconnection lengths a priori (very early in the design flow) therefore gain attention and will become important for making the right design decisions when one still has the freedom to do so. However, at that time, one also knows least about the possible results of subsequent design steps. Conventional models for a priori estimation of wire lengths in computer chips use Rent's rule to estimate the number of terminals needed for communication between sets of gates. The number of interconnections then follows by taking into account that most nets are point-to-point connections. In this paper, we apply our previously introduced model for multiterminal nets to show that such nets have a fundamentally different influence on the wire length estimations than point-to-point nets. We then estimate the wire length distribution of Steiner tree lengths for applications related to routing resource estimation. Experiments show that the new estimated Steiner-length distributions capture the multiterminal effects much better than the previous point-to-point length distributions. The accuracy of the estimated values is still too low, as for the conventional point-to-point models, because we are still lacking a good model for placement optimization. However, the new results are a step closer to the application of wire length estimation techniques in real-world situations.

Guest editorial: System-level interconnect prediction

for hierarchically placed cells. The new approach splits nets into two-terminal segments and develops a technique based on a generating polynomial representation of the segment lengths to correctly calculate the Steiner length of the reconstructed net. The generating polynomial representation allows all possible net segment length combinations to be computed in an efficient manner and results in a net length averaged over all equally likely routing alternatives. The final two contributions to the special section are on the application of SLIP techniques to the optimal design and layout of programmable logic devices. The paper by Rahman et al. addresses methods for the design of an SRAM-based programmable gate array routing architecture. It proposes an optimal design in which the range of predefined wire lengths approximates the wire length distribution estimate of a representative netlist. The problem is thus transformed into a Rentian wire length estimation problem. Since it is based on an analytical model, the extension of the analysis to the design of three-dimensional (3-D) architectures with 3-D routing switches is also considered. The final brief by Hutton

A comparison of various terminal-gate relationships for interconnect prediction in VLSI circuits

Over the years, different interpretations of Rent's rule and different ways of estimating the Rent parameters have emerged. In general, these parameters are extracted from the average terminal-gate relationship for a set of circuit modules. We show that this relationship (the Rent characteristic) strongly depends on the definition of the circuit modules. These can be generated in many different ways, either from the topology of the circuit graph or, in a geometric way, by cutting regions from a circuit layout. The resulting Rent parameters can be quite far apart. This paper discusses the fundamental differences between the topological and the two geometric interpretations of the Rent characteristic that are expected to be most appropriate for current wirelength estimation techniques. Our discussion is based on experimental data, as well as on a theoretical model that can be used to estimate certain geometric Rent characteristics from the topological Rent parameters. Using this model, we derive a theoretical lower limit to the value of the average geometric Rent exponent. We also study the impact of the placement approach and placement quality on the geometric Rent characteristics.

Toward better wireload models in the presence of obstacles

Wirelength estimation techniques typically contain a site density function that enumerates all possible path sites for each wirelength in an architecture and an occupation probability function that assigns a probability to each of these paths to be occupied by a wire. In this paper, we apply a generating polynomial technique to derive complete expressions for site density functions which take effects of layout region aspect ratio and the presence of obstacles into account. The effect of an obstacle is separated into two parts: the terminal redistribution effect and the blockage effect. The layout region aspect ratio and the obstacle area are observed to have a much larger effect on the wirelength distribution than the obstacle's aspect ratio and location. Accordingly, we suggest that these two parameters be included as indices of lookup tables in wireload models. Our results apply to a priori wirelength estimation schemes in chip planning tools to improve parasitic estimation accuracy and timing closure; this is particularly relevant for system-on-chip designs where IP blocks are combined with row-based layout.

Congestion estimation during top-down placement

Congestion is one of the fundamental issues in very large scale integration physical design. In this paper, we propose two congestion-estimation approaches for early placement stages. First, we theoretically analyze the peak-congestion value of the design and experimentally validate the estimation approach. Second, we estimate regional congestion at the early stages of top-down placement. This is done by combining the wire-length distribution model and interregion wire estimation. Both approaches are based on the well-known Rent's rule, which is previously used for wirelength estimation. This is the first attempt to predict congestion using Rent's rule. The estimation results are compared with the layout after placement and global routing. Experiments on large industry circuits show that the early congestion estimation based on Rent's rule is a promising approach.