3173724
Buffer insertion in large circuits with constructive solution search techniques
Most existing buffer insertion algorithms, such as van Ginneken's algorithm, consider only individual nets. As a result, these algorithms tend to over buffer when applied to combinational circuits, since it is difficult to decide how many buffers to insert in each net. Recently, Sze, et al. (Sze, 2005) proposed a path-based algorithm for buffer insertion in combinational circuits. However their algorithm is inefficient for large circuits when there are many critical paths. In this paper, we present a new buffer insertion algorithm for combinational circuits such that the timing requirements are met and the buffer cost is minimized. Our algorithm iteratively inserts buffers in the circuit to improve the circuit delay. The core of this algorithm is simple but effective technique that guides the search for a good buffering solution. Experimental results on ISCAS85 circuits show that our new algorithm on average uses 36% less buffers and runs 3 times faster than Sze's algorithm
130258
Longest-path selection for delay test under process variation
Under manufacturing process variation, a path through a fault site is called longest for delay test if there exists a process condition under which the path has the maximum delay among all paths through that fault site. There are often multiple longest paths for each fault site in the circuit, due to different process conditions. To detect the smallest delay fault, it is necessary to test all longest paths through the fault site. However, previous methods are either inefficient or their results include too many paths that are not longest.This paper presents an efficient method to generate the longest path set for delay test under process variation. To capture both structural and systematic process correlation, we use linear delay functions to express path delays under process variation. A novel path-pruning technique is proposed to discard paths that are not longest, resulting in a significantly reduction in the number of paths compared with the previous best method. The new method can be applied to any process variation as long as its impact on delay is linear.
195989392
Process variation dimension reduction based on SVD.
We propose an algorithm based on singular value decomposition (SVD) to reduce the number of process variation variables. With few process variation variables, fault simulation and timing analysis under process variation can be performed efficiently. Our algorithm reduces the number of process variation variables while preserving the delay function with respect to process variation. Compared with the principal component analysis (PCA) method, our algorithm requires less computation time and guarantees the reduced process variation variables are independent. Experimental results on ISCAS85 circuits show that the algorithm works well. 1 INTROCUTION In modern multi-layer VLSI circuits, the dimension of the process variation is large. For example, in a k-metal technology, there are 2k variables for metal width and thickness, k variables for inter-layer dielectric (ILD) thickness, a gate length variable, and some other variables. With such a large number of process variation variables, timing analysis under process variation is very time consuming, and may not find the worst-case process corner [1][2]. In this paper, we propose the novel concept of variation dimension reduction. The idea is originated from the following observation. For different nets, the underlying process variation variables are the same. Therefore, the delays of the nets are correlated. We model the delay from an input pin of a cell to an input pin of a downstream cell, also known as the buffer-to-buffer delay, as a linear function of process variation variables: d = dnominal(1 + a1x1 + a2x2 + ... + anxn), where x1, x2, ..., xn are process variation variables, a1, a2, ..., an are their corresponding coefficients, and dnominal is the nominal delay. For different nets, the coefficients are different, but the process variation variables are the same. The assumption that the delay is linear with respect to each process variation variable is supported by SPICE simulation of real circuits within reasonable ranges of the process variation [3]. There are many forms of process variation [4][5]. In this paper, we only consider systematic process variation and assume the process variation variables among different nets are fully correlated. We assume the following variation ranges: metal thickness ±20%, metal width ±10%, ILD thickness ±40%, and gate length ±10%. To obtain the delay function with respect to process variation, we first extract interconnect parasitic from the layout and compute the nominal buffer-to-buffer delay for all nets. Then for each process variation variable, we modify the layout or the technology file by varying a specified amount (for example, +10% for metal1 thickness), and perform RC extraction and delay evaluation for the modified layout. The coefficient for this process variation variable is obtained by interpolating the two delays. Recently, the principal component analysis (PCA) method was used to reduce the dimension of process variation [7]. It was shown to be effective for analyzing analog circuits under process variation. However, the PCA method is inefficient for digital circuits, because the PCA method constructs and solves a correlation matrix of size mn×mn, where n is the number of process variation variables and m is the number of nets or devices. For digital circuits, m is easily in hundreds or thousands. In this paper, we propose a new method based on singular value decomposition (SVD) [6]. Our algorithm detects the linear dependence and reduces the number of process variation variables, while minimizing the average error of the delay. Note that although the PCA method also uses SVD, their matrix is size mn×mn while ours is size m×n. To make the reduced process variables linearly/statistically independent, which is desirable for fault simulation and timing analysis, we also propose a sub-matrix SVD method. In Section 2, the SVD method and sub-matrix SVD method for dimension reduction are given. In Section 3, we show the experimental results. It shows that if we simply pick the most important process variation variables and discard the rest, then the average error of net delay is twice as much as the average error produced by our algorithm. 2 ALGORITHM 2.1 Singular Value Decomposition (SVD) The SVD method is based on the following theorems [6]. Theorem 1 If A is an m×n matrix, then there exist orthogonal m×m matrix U=[u1,...,um] and n×n matrix V=[v1,...,vn], such that U·A·V=diag(σ1,...,σp), which is an m×n matrix, p=min{m,n}, and σ1 ≥ σ2 ≥...≥ σp ≥ 0. The σi’s are the singular values of A, and vectors ui and vi are the ith left and right singular vector, respectively. The process to find U and V is called SVD. It can be done by the Golub-Reinsch algorithm of time complexity O(mn+mn+n) [6] (pp. 254). To compute U(:,1:n) =[u1,...,un], which is an m×n (m>n) matrix, the time complexity is O(mn+n) [6]. Theorem 2 Let the SVD of m×n matrix A be defined in Theorem 1. If r < rank(A) and let ∑ = = r i T i i i v u A 1 * σ , then 1 2 * 2 ) ( min + = = − = − r r B rank A A B A σ . In other words, A is the best 2-norm approximation of A among all rank r matrices. 2.2 Application to Dimension Reduction We are given the delay of m nets represented as Ax, where A is an m×n matrix, n is the number of process variation variables, x=[x1,...,xn] is the vector of process variation variables, and xi’s are independent of each other. From Theorem 2, A=U(:,1:r)·S·V(:,1:r), where S=diag(σ1,...,σr), U(:,1:r)=[u1,...,ur], and V(:,1:r) =[v1,...,vr]. Therefore, Ax≈Ax=U(:,1:r)·S·V(:,1:r)x=Bz, where B=U(:,1:r)·S is an m×r matrix and z=V(:,1:r)x is an r×1 vector. Since the dimension of B is much less than the dimension of A, we use Bz to approximate Ax. If we just want to reduce the number of process variation variables, then Bz is the resulting delay function, and z is the vector of new process variation variables. However, we often have an additional requirement from circuit simulation that the new process variation variables z1, ..., zr must be independent. For example, if z1=x1−x2+x3 and z2=x1+x2−x3, then z1 and z2 are not independent although the number of variables is reduced from 3 to 2. 2.3 Sub-Matrix SVD (SMSVD) We propose a sub-matrix SVD method (SMSVD) to ensure the independence between zi’s. The basic idea is to partition columns of A into r sub-matrices, and then use SVD on each sub-matrix. The following is the algorithm: 1) Partition A into sub-matrices A1, A2, ..., Ar, where A=[A1, A2,..., Ar]. Ai is an m×qi matrix, i=1,..., r. 2) For i=1,..., r, compute the approximation matrix Ai of Ai through SVD in which the approximation rank is 1. Define SVD of Ai as Ui·Ai·Vi=diag(σi1,...,σip), then Ai=Ui(:,1)·σi1·Vi(:,1) and ║Ai−Ai║2=σi2. 3) Construct B=[U1(:,1)σ11, U2(:,1)σ21, ..., Ur(:,1)σr1],
13162337
A circuit level fault model for resistive opens and bridges
Delay faults are an increasingly important test challenge. Traditional open and bridge fault models are incomplete because only the functional fault or a subset of delay fault are modeled. In this paper, we propose a circuit level model for resistive open and bridge faults. All possible fault behaviors are illustrated and a general resistive bridge delay calculation method is proposed. The new models are practical and easy to use. Fault simulation results show that the new models help the delay test to catch more bridge faults.
5937656
Complexity analysis and speedup techniques for optimal buffer insertion with minimum cost
As gate delays decrease faster than wire delays for each technology generation, buffer insertion becomes a popular method to reduce the interconnect delay. Several modern buffer insertion algorithms (e.g., [7, 6, 15]) are based on van Ginneken's dynamic programming paradigm [14]. However, van Ginneken's original algorithm does not control buffering resources and tends to over-buffering, thereby wasting area and power. It has been a major open problem whether it is possible to optimize slack and at the same time minimize the buffer usage.This paper settles this open problem by showing that for arbitrary integer cost functions, the problem is NP-complete. We also extend the pre-buffer slack technique [12] to minimize the buffer cost. This technique can significantly reduce the running time and memory in buffer cost minimization problem. The experimental results show that our algorithm can speed up the running time up to 17 times and reduces the memory to 1/30 of traditional best know algorithm. Finally, we show how to efficiently deal with multiway merge in buffer insertion.
62540162
Longest-path selection for delay test under process variation
Under manufacturing process variation, a path through a net is called longest if there exists a process condition under which the path has the maximum delay among all paths through the net. There are often multiple longest paths for each net, due to different process conditions. In addition, a local defect, such as resistive open or a resistive bridge, increases the delay of the affected net. To detect delay faults due to local defects and process variation, it is necessary to test all longest paths through each net. Previous approaches to this problem were inefficient because of the large number of paths that are not longest. This paper presents an efficient method to generate the set of longest paths for delay test under process variation. To capture both structural and process correlation between path delays, we use linear delay functions to express path delays under process variation. A novel technique is proposed to prune paths that are not longest, resulting in a significant reduction in the number of paths. In experiments on International Symposium on Circuits and Systems (ISCAS) circuits, our number of longest paths is 1-6% of the previous best approach, with 300/spl times/ less running time.
1327847
On achieving maximum multicast throughput in undirected networks
The transmission of information within a data network is constrained by the network topology and link capacities. In this paper, we study the fundamental upper bound of information dissemination rates with these constraints in undirected networks, given the unique replicable and encodable properties of information flows. Based on recent advances in network coding and classical modeling techniques in flow networks, we provide a natural linear programming formulation of the maximum multicast rate problem. By applying Lagrangian relaxation on the primal and the dual linear programs (LPs), respectively, we derive a) a necessary and sufficient condition characterizing multicast rate feasibility, and b) an efficient and distributed subgradient algorithm for computing the maximum multicast rate. We also extend our discussions to multiple communication sessions, as well as to overlay and ad hoc network models. Both our theoretical and simulation results conclude that, network coding may not be instrumental to achieve better maximum multicast rates in most cases; rather, it facilitates the design of significantly more efficient algorithms to achieve such optimality.
15936335
A divide-and-conquer 2.5-D floorplanning algorithm based on statistical wirelength estimation
An efficient and effective divide-and conquer 2.5D floorplanning algorithm is proposed for wirelength optimization. Modules are pre-partitioned into different dies with respect to the statistical wirelength estimation result. Then a floorplan is generated on each die for wirelength optimization. The new partitioning method successfully solves the conflict between wirelength minimization and inter-die via constraints. Experimental results show that our algorithm could provide noticeable improvement in the total wirelength compared to both 2D design and the previous 2.5D floorplanning algorithm.
15181003
An Efficient Sort-Based DDM Matching Algorithm for HLA Applications with a Large Spatial Environment
Simulation is a low cost and safe alternative to solve complex problems in various areas. To promote reuse and interoperability of simulation applications and link geographically dispersed simulation components, distributed simulation was introduced. The high level architecture (HLA) is the IEEE standard for distributed simulation. To optimize communication efficiency between simulation components, HLA defines a data distribution management (DDM) service group for filtering out unnecessary data exchange. It relies on the computation of overlap between update and subscription regions, which is called matching. In this paper, we propose an efficient sort-based DDM matching algorithm for HLA applications with a large spatial environment. A theoretical analysis of our algorithm concludes that it should have good storage and computational scalability. The experimental results have verified the theoretical conclusions by showing that our algorithm has much less storage requirement than the original sort-based matching algorithm and generally has the best computational performance when compared with region-based and the original sort-based matching algorithms.
3705333
Rate-distortion optimal video summary generation
The need for video summarization originates primarily from a viewing time constraint. A shorter version of the original video sequence is desirable in a number of applications. Clearly, a shorter version is also necessary in applications where storage, communication bandwidth, and/or power are limited. The summarization process inevitably introduces distortion. The amount of summarization distortion is related to its "conciseness", or the number of frames available in the summary. If there are m frames in the original sequence and n frames in the summary, we define the summarization rate as m/n, to characterize this "conciseness". We also develop a new summarization distortion metric and formulate the summarization problem as a rate-distortion optimization problem. Optimal algorithms based on dynamic programming are presented and compared experimentally with heuristic algorithms. Practical constraints, like the maximum number of frames that can be skipped, are also considered in the formulation and solution of the problem.
4499601
Impact of data compression on energy consumption of wireless-networked handheld devices
We investigate the use of data compression to reduce the battery consumed by handheld devices when downloading data from proxy servers over a wireless LAN. To make a careful trade-off between the communication energy and the overhead to perform decompression, we experiment with three universal lossless compression schemes, using a popular handheld device in a wireless LAN environment and we find interesting facts. The results show that, from the battery-saving perspective, the gzip compression software (based on LZ77) to be far superior to bzip2 (based on BWT) and compress (based on LZW). We then present an energy model to estimate the energy consumption for the compressed downloading. With this model, we further reduce the energy cost of gzip by interleaving communication with computation and by using a block-by-block selective scheme based on the compression factor of each block. We also use a threshold file size below which the file is not to be compressed before transferring.