S. W. Hadley, B. L. Mark, and A. Vannelli, "An Efficient Eigenvector Approach for Finding Netlist Partitions", IEEE Trans. on CAD 11(7), July 1992, pp. 885-892.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....MODEL BASED DECOMPOSITION OF DESIGN PROBLEMS 12 hyperedge model overestimates the number of hyperedges cut by a partition. For example, in Figure 4 with w = 1 3 , the estimated number of hyperedges cut by the partition P 2 = v 1 , v 4 , v 2 , v 3 is 4 3 instead of 1. b) Hadley et al. [28] proposed a hyperedge model in which the total weight of the edges of graph G that are cut by any vertex partition is not greater than the number of hyperedges of the associated hypergraph H cut by the same partition. So this hyperedge model underestimates the number of hyperedges cut by a ....

S. Hadley, B. Mark, and A. Vannelli, "An Efficient Eigenvector Approach for Finding Netlist Partitions," IEEE Transactions on Computer-Aided Design, Vol. 11, No. 7, pp. 885--892, 1992.

.... The relation between the properties of a graph and its spectrum (the eigenvalues eigenvectors of its associated matrices) has been an area of active research for several years [13, 8, 16, 20] The spectra of the adjacency matrix A or the Laplacian Q of a graph are the basis for both partitioning [3, 9, 12] and placement techniques [11] III B Spectral ratio cut partitioning using the Laplacian Q Spectral partitioning forms clusters of vertices based on the embedding implied by the eigenvectors V of a graph matrix, which can be the Laplacian Q, or the adjacency matrix A of the graph. To minimize ....

S. W. Hadley, B. L. Mark, and A. Vanelli. An Efficient Eigenvector Approach for Finding Netlist Partitions. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, CAD-11(7):885--892, July 1992.

....tend to get trapped in locally optimal partitions. To avoid locally minimal partitions, interchanges are performed from multiple random initial partitions. The best result is selected as the final 1 the work of the second author was partially supported by a NSERC graduate scholarship. partition [7]. Meta heuristics are used to guide interchange heuristics out of locally optimal partitions [8] Another technique is to start from good initial partitions [7, 8, 9] Unlike partitioning heuristics, clustering heuristics identify and merge strongly connected cells into clusters, condensing the ....

....best result is selected as the final 1 the work of the second author was partially supported by a NSERC graduate scholarship. partition [7] Meta heuristics are used to guide interchange heuristics out of locally optimal partitions [8] Another technique is to start from good initial partitions [7, 8, 9]. Unlike partitioning heuristics, clustering heuristics identify and merge strongly connected cells into clusters, condensing the circuit. Clustering and partitioning may be implemented as a two phase partitioning heuristic. The circuit is initially clustered. Cell interchanges are applied to the ....

S. W. Hadley, B. L. Mark, and A. Vannelli. An efficient eigenvector approach for finding netlist partitions. IEEE Trans. of Computer-Aided Design, 11(7):885--892, July 1992.

....from a flat netlist of the design. Due to this step all design information like hierarchy, celltypes of nodes or clocked nets and other useful information is lost. Only the number of nets is used to weight graph edges, sometimes employing timing information or complex graph weighting models [HaMa92]. Although nodes could be individually weighted, in most cases the weight is set to one. But information about modules and nets are the most important aspects designers use to manually partition a design and thereby getting better results than any automated algorithm 4) Grow clusters with free ....

Hadley S.W.; Mark B.L.; Vannelli A.; "An Efficient Eigenvector Approach for Finding Netlist Partitions", IEEE Transactions on Computer Aided Design, vol. 11, no. 7, pp. 885-892, 1992

....of hyperedges cut by a partition. For example, in Figure 4 with w = 1 3 , the estimated number of hyperedges cut by the partition P 2 = v 1 , v 4 , v 2 , v 3 is 4 3 instead of 1. A HYPERGRAPH FRAMEWORK FOR OPTIMAL MODEL BASED DECOMPOSITION OF DESIGN PROBLEMS 12 (b) Hadley et al. [28] proposed a hyperedge model in which the total weight of the edges of graph G that are cut by any vertex partition is not greater than the number of hyperedges of the associated hypergraph H cut by the same partition. So this hyperedge model underestimates the number of hyperedges cut by a ....

S. Hadley, B. Mark, and A. Vannelli, "An Efficient Eigenvector Approach for Finding Netlist Partitions," IEEE Transactions on Computer-Aided Design, Vol. 11, No. 7, pp. 885--892, 1992. A HYPERGRAPH FRAMEWORK FOR OPTIMAL MODEL-BASED DECOMPOSITION OF DESIGN PROBLEMS 34

....for airfoils, dual is the dual of the Delauney triangulation, comm is the communication graph used in [27] shuttle: connectivity for some large finite element problems, collected by Dawson Deuermeyer, CRAY Res. in [11] The second group of data was provided to us by S. Areibi and A. Vannelli [2, 13]. This data represents hypergraph partitioning problems, where hyperedges are represented by cliques, which underestimate cuts in the original hypergraph. These problems come from netlist partitioning problems which arise from chip layout. The results are not significantly different from our ....

S.W. HADLEY, B.L. MARK, and A. VANNELLI. An efficient eigenvector approach for finding netlist partitions. IEEE Transactions on Computer-Aided Design, 11:885--892, 1992.

....The graph partitioning problem is well known to be NP hard and therefore finding an optimal solution is likely very difficult. Yet this problem has many applications in various areas. One important application is VLSI design; see e.g. LEN90] for a survey of Integrated Circuit Layout. See also [HMV92] for its application to netlist partition. One popular and very successful heuristic for finding good partitions was proposed by Kernighan and Lin [KL70] in 1970. In the early 70 s Donath and Hoffman [DH73] provided an eigenvalue based bound. Several new eigenvalue based bound techniques were ....

S.W. HADLEY, B.L. MARK, and A. VANNELLI. An efficient eigenvector approach for finding netlist partitions. IEEE Transactions on Computer-aided Design, 11 No. 7:885--892, 1992.

....corresponding modules. Following ideas of Hall [12] our approach embeds the netlist into d dimensional Euclidean space via the well established relationship between eigenvectors of the netlist Laplacian 2 and minimum ratio cut partitionings (or minimum squared wirelength placements) see [11] [9] for surveys) Every eigenvector of the Laplacian gives a distinct, one dimensional spatial embedding of the circuit graph wherein strongly connected modules will tend to be placed close to each other. Because the squared wirelength of each eigenvector placement is given by its corresponding ....

.... 5 4 3 2 RSBipart [4] 48.8 44.5 40.6 37.1 41.0 36.6 27.3 14.6 KP (Chan et al. 4] 45.0 51.1 32.1 36.8 25.9 25.7 15.9 13.5 AGG 2 [14] 33.1 31.7 29.8 24.8 26.0 17.4 17.9 13.5 KC 2 [8] 34.6 33.6 34.4 30.7 27.5 16.4 17.4 13.5 Single Linkage 1 [14] 49.5 39.2 39.9 23.7 13.5 Divisive Min Diameter 2 [9] 59.5 46.8 42.9 32.8 13.5 Divisive Sum Diameters 3 [13] 96.0 74.9 59.8 72.3 13.5 Agglom Sum Diameters 3 154.5 127.2 88.3 72.3 13.5 Table 1: Comparison of the various clustering objectives and algorithms for the Primary1 benchmark netlist, using the partitioning specific net model in ....

S. W. Hadley, B. L. Mark and A. Vanelli, "An Efficient Eigenvector Approach for Finding Netlist Partitions", in IEEE Trans. on CAD, 11(7), July 1992, pp. 885-892.

....are practically possible should be used to construct a solution. This philosophy is in contrast to that of the widely used spectral bipartitioning (SB) heuristic (which uses a single eigenvector to construct a 2 way partitioning) and several previous multiway partitioning heuristics [7] 10] 16] [26] [37] which use k eigenvectors to construct a k way partitioning) Our result motivates a simple ordering heuristic that is a multiple eigenvector extension of SB. This heuristic not only significantly outperforms SB, but can also yield excellent multi way VLSI circuit partitionings as compared ....

....is zero rounding error, the optimum cut value equal to a weighted sum of the largest k eigenvalues (of the adjacency matrix) 16] is obtained. An extension of Barnes approach has been given by Rendl and Wolkowicz [37] and iterative improvement post processing was proposed by Hadley et al. [26]. ffl Points in d dimensional space: Hall [27] proposed using the coordinates of the second and third eigenvectors of the Laplacian to construct a 2 dimensional placement. Alpert and Kahng [1] extended this idea to higher dimensions, i.e. the i th entries of d eigenvectors yield the ....

S. W. Hadley, B. L. Mark, and A. Vannelli, An efficient eigenvector approach for finding netlist partitions, IEEE Trans. on CAD 11 (1992) 885-892.

....is likely very difficult. Yet this problem has many applications. One important application is VLSI design; see e.g. 10] for a survey of Integrated Circuit Layout. One popular and very successful heuristic for finding good partitions was proposed by Kernighan and Lin [9] in 1970. See also [5] for its application on netlist partitioning. In the early 70 s Donath and Hoffman [3] provided an eigenvalue based bound for (GP) Several new eigenvalue based bounds were presented by F. Rendl and H. Wolkowicz in [11] a computational study showed these bounds to be very good, see e.g [4] A ....

S.W. HADLEY, B.L. MARK, and A. VANNELLI. An efficient eigenvector approach for finding netlist partitions. IEEE Transactions on Computer-Aided Design, 11:885--892, 1992.

....V = fv 1 ; v 2 ; vng to denote either the modules of the netlist or the points of the geometric embedding, i.e. v i can denote either a netlist module or a point in d . We overload these meanings for notational convenience; the meaning should be clear from the context. in, e.g. [23] [25] ffl Finally, we describe the DP RP algorithm which uses dynamic programming to optimally solve the RP formulation for various objective functions in the literature. These objectives include Scaled Cost [12] Absorption [44] and diameter related objectives. DP RP can transparently handle ....

....the partitioning specific net model with edge weight 4 p(p Gamma1) for a p pin net 3 ) ffl The first d eigenvectors corresponding to the smallest nonzero eigenvalues of the Laplacian of G(V; EG ) are then used to embed the netlist into d dimensions. As with previous works of [12] [23] [25] we are motivated by the well established relationships between eigenvectors of a graph s Laplacian and either min cut partitionings or minimum squared edgelength placements of the graph (see, e.g. 4] for a concise overview) Let 1 ; 2 ; n be the n eigenvectors of Q ....

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S. W. Hadley, B. L. Mark and A. Vanelli, "An Efficient Eigenvector Approach for Finding Netlist Partitions", IEEE Trans. on CAD, Vol. 11, No. 7, pp. 885-892, July 1992.

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S. W. Hadley, B. L. Mark, and A. Vannelli, "An Efficient Eigenvector Approach for Finding Netlist Partitions", IEEE Trans. on CAD 11(7), July 1992, pp. 885-892.

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S. W. Hadley, B. L. Mark, and A. Vannelli. An efficient eigenvector approach for finding netlist partitions. IEEE Transactions on Computer-Aided Design, pages 885--92, July 1992.

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Hadley, S., Mark, B., and Vannelli, A., 1992, "An Efficient Eigenvector Approach for Finding Netlist Partitions," IEEE Transactions on Computer-Aided Design, Vol. 11, No. 7, pp. 885--892.

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