As technology advances apace, crosstalk becomes a design metric of comparable importance to area and delay. This article focuses mainly on the crosstalk issue, specifically on the impacts of physical design and process variation on crosstalk. While the feature size shrinks below 0.25 μm, the impact of process variation on crosstalk increases rapidly. Hence, a crosstalk insensitive design is desirable in the deep submicron regime. In this article, crosstalk sensitivity is referred to as the influence of process variation on crosstalk in a circuit. We show that the lower bound of crosstalk sensitivity grows quadratically, while that of crosstalk increases linearly. Therefore, designers should also consider crosstalk sensitivity, when optimizing other design objectives such as crosstalk, area, and delay. According to our modeling, these objectives are all in posynomial forms, and thus the multiobjective optimization problem can optimally be solved by Lagrangian relaxation. Experimental results show that our method is effective and efficient. For instance, a circuit of 2856 gates and 5272 wires is optimized using 13-minute runtime and 2.8-MB memory on a Pentium III 1.0 GHz PC with 256-MB memory. In particular, by relaxing Lagrange multipliers to the critical paths, it takes only two iterations for all solutions to converge to the global optimal, which is much more efficient than related previous work. This relaxation scheme provides a key insight into the rapid convergence in Lagrangian relaxation.

As technology advances apace, crosstalk becomes a design metric of comparable importance to area and delay. This article focuses mainly on the crosstalk issue, specifically on the impacts of physical design and process variation on crosstalk. While the feature size shrinks below 0.25μ m , the impact of process variation on crosstalk increases rapidly. Hence, a crosstalk insensitive design is desirable in the deep submicron regime. In this article, crosstalk sensitivity is referred to as the influence of process variation on crosstalk in a circuit. We show that the lower bound of crosstalk sensitivity grows quadratically, while that of crosstalk increases linearly. Therefore, designers should also consider crosstalk sensitivity, when optimizing other design objectives such as crosstalk, area, and delay. According to our modeling, these objectives are all in posynomial forms, and thus the multi-objective optimization problem can optimally be solved by Lagrangian relaxation. Experimental results show that our method is effective and efficient. For instance, a circuit of 2856 gates and 5272 wires is optimized using 13-minute runtime and 2.8-MB memory on a Pentium III 1.0 GHz PC with 256-MB memory. In particular, by relaxing Lagrange multipliers to the critical paths, it takes only two iterations for all solutions to converge to the global optimal, which is much more efficient than related previous work. This relaxation scheme provides a key insight into the rapid convergence in Lagrangian relaxation.

Architecture and CAD are closely related issues in FPGA design. Routing architecture design shall optimize routability and facilitate router development; on the other hand, router design shall consider the specific properties of routing architectures to optimize the performance of the router. In this paper, we propose effective and efficient unified matching-based algorithms for array-based FPGA routing and segmentation design. For the segmentation design, we consider the similarity of input routing instances and formulate a net-matching problem to construct the optimal segmentation architecture. For the router design, we present a matching-based timing-driven routing algorithm which can consider a versatile set of routing segments. Experimental results show that our designed segmentations significantly outperform those used in commercially available FPGAs. For example, our designed segmentations achieve, on average, 14.6% and 19.7% improvements in routability, compared with those used in the Lucent Technologies ORCA 2C-series and the Xilinx XC4000E-series FPGAs, respectively.

As the operating frequency increases to Giga Hertz and the rise time of a signal is less than or comparable to the time-of-jiight delay of a line, it is necessay to consider the transmission line behavior for delay computation, We present in this paper an analytical formula for the delay Computation under the transmission line model. Extensive simulations with SPICE show the high fidelity ojthe formula. Compared with previous works [S, I I], our model leads to smaller average errors in delay estimation. Based on this formula, we show the propern, that the minimum delay for a transmission line with rejection occurs when the number of round trips is minimized (i.e., equals one). Besides, we show that the delay of a circuit path is a posynomial function in wire and buffer sizes, implving that a local optimum is equal to the global optimum. Thus, we can apply any ejicient search algorithm such as the well-known gradient search procedure to compute the globally optimal solution. Experimental results show that simultaneous wire and buffer sizing is venl effective for perjormance optimization under the transmission line model. 'tu;: the width of wire z. 2;: the length of wire z. Z,: the characteristic impedance of wire z. 21%: the propagation velocity of wire z. R,: the resistance of source. CL : the capacitance of load. VD D : the high voltage of power supply. K: the threshold voltage.( I ' , ~: the transmission coefficient at point i if a signal is transmitted from point z to point j.

Architecture and CAD are closely related issues in FPGA design. Routing architecture design shall optimize routability and facilitate router development; on the other hand, router design shall consider the specific properties of routing architectures to optimize the performance of the router. In this paper, we propose effective and efficient unified matching-based algorithms for array-based FPGA routing and segmentation design. For the segmentation design, we consider the similarity of input routing instances and formulate a net-matching problem to construct the optimal segmentation architecture. For the router design, we present a matching-based timing-driven routing algorithm which can consider a versatile set of routing segments. Experimental results show that our designed segmentations significantly outperform those used in commercially available FPGAs. For example, our designed segmentations achieve, on average, 14.6% and 19.7% improvements in routability, compared with those used in the Lucent Technologies ORCA 2C-series and the Xilinx XC4000E-series FPGAs, respectively.