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134
New spectral methods for ratio cut partition and clustering
 IEEE Trans. on ComputerAided Design
, 1992
"... AbstractPartitioning of circuit netlists is important in many phases of VLSI design, ranging from layout to testing and hardware simulation. The ratio cut objective function [29] has received much attention since it naturally captures both mincut and equipartition, the two traditional goals of par ..."
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Cited by 286 (16 self)
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AbstractPartitioning of circuit netlists is important in many phases of VLSI design, ranging from layout to testing and hardware simulation. The ratio cut objective function [29] has received much attention since it naturally captures both mincut and equipartition, the two traditional goals of partitioning. In this paper, we show that the second smallest eigenvalue of a matrix derived from the netlist gives a provably good approximation of the optimal ratio cut partition cost. We also demonstrate that fast Lanczostype methods for the sparse symmetric eigenvalue problem are a robust basis for computing heuristic ratio cuts based on the eigenvector of this second eigenvalue. Effective clustering methods are an immediate byproduct of the second eigenvector computation, and are very successful on the “difficult ” input classes proposed in the CAD literature. Finally, we discuss the very natural intersection graph
Multilevel kway Hypergraph Partitioning
, 1999
"... In this paper, we present a new multilevel kway hypergraph partitioning algorithm that substantially outperforms the existing stateoftheart KPM/LR algorithm for multiway partitioning, both for optimizing local as well as global objectives. Experiments on ..."
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Cited by 160 (9 self)
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In this paper, we present a new multilevel kway hypergraph partitioning algorithm that substantially outperforms the existing stateoftheart KPM/LR algorithm for multiway partitioning, both for optimizing local as well as global objectives. Experiments on
Multilevel Circuit Partitioning
 IN PROC. OF THE 34TH ACM/IEEE DESIGN AUTOMATION CONFERENCE
, 1998
"... Many previous works in partitioning have used some underlying clustering algorithm to improve performance. As problem sizes reach new levels of complexity, a single application of a clustering algorithm is insufficient to produce excellent solutions. Recent work has illustrated the promise of multi ..."
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Cited by 88 (8 self)
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Many previous works in partitioning have used some underlying clustering algorithm to improve performance. As problem sizes reach new levels of complexity, a single application of a clustering algorithm is insufficient to produce excellent solutions. Recent work has illustrated the promise of multilevel approaches. A multilevel partitioning algorithm recursively clusters the instance until its size is smaller than a given threshold, then unclusters the instance while applying a partitioning refinement algorithm. In this paper, we propose a new multilevel partitioning algorithm that exploits some of the latest innovations of classical iterative partitioning approaches. Our method also uses a new technique to control the number of levels in our matchingbased clustering algorithm. Experimental results show that our heuristic outperforms numerous existing bipartitioning heuristics with improvements ranging from 6.9 to 27.9 % for 100 runs and 3.0 to 20.6 % for just ten runs (while also using less CPU time). Further, our algorithm generates solutions better than the best known mincut bipartitionings for seven of the ACM/SIGDA benchmark circuits, including golem3 (which has over 100 000 cells). We also present quadrisection results which compare favorably to the partitionings obtained by the GORDIAN cell placement tool. Our work in multilevel quadrisection has been used as the basis for an effective cell placement package.
Spectral Partitioning: The More Eigenvectors, the Better
 PROC. ACM/IEEE DESIGN AUTOMATION CONF
, 1995
"... The graph partitioning problem is to divide the vertices of a graph into disjoint clusters to minimize the total cost of the edges cut by the clusters. A spectral partitioning heuristic uses the graph's eigenvectors to construct a geometric representation of the graph (e.g., linear orderings) w ..."
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Cited by 75 (3 self)
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The graph partitioning problem is to divide the vertices of a graph into disjoint clusters to minimize the total cost of the edges cut by the clusters. A spectral partitioning heuristic uses the graph's eigenvectors to construct a geometric representation of the graph (e.g., linear orderings) which are subsequently partitioned. Our main result shows that when all the eigenvectors are used, graph partitioning reduces to a new vector partitioning problem. This result implies that as many eigenvectors as are practically possible should be used to construct a solution. This philosophy isincontrast to that of the widelyused spectral bipartitioning (SB) heuristic (which uses a single eigenvector to construct a 2way partitioning) and several previous multiway partitioning heuristics [7][10][16][26][37] (which usek eigenvectors to construct a kway partitioning). Our result motivates a simple ordering heuristic that is a multipleeigenvector extension of SB. This heuristic not only signi cantly outperforms SB, but can also yield excellent multiway VLSI circuit partitionings as compared to [1] [10]. Our experiments suggest that the vector partitioning perspective opens the door to new and effective heuristics.
Multilevel hypergraph partitioning
 Applications in VLSI design, ACM/IEEE Design Automation Conference
, 1997
"... Traditional hypergraph partitioning algorithms compute a bisection a graph such that the number of hyperedges that are cut by the partitioning is minimized and each partition has an equal number of vertices. The task of minimizing the cut can be considered as the objective and the requirement that t ..."
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Cited by 74 (3 self)
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Traditional hypergraph partitioning algorithms compute a bisection a graph such that the number of hyperedges that are cut by the partitioning is minimized and each partition has an equal number of vertices. The task of minimizing the cut can be considered as the objective and the requirement that the partitions will be of the same size can be considered as the constraint. In this paper we extend the partitioning problem by incorporating an arbitrary number of balancing constraints. In our formulation, a vector of weights is assigned to each vertex, and the goal is to produce a bisection such that the partitioning satisfies a balancing constraint associated with each weight, while attempting to minimize the cut. We present new multiconstraint hypergraph partitioning algorithms that are based on the multilevel partitioning paradigm. We experimentally evaluate the effectiveness of our multiconstraint partitioners on a variety of synthetically generated problems.
Teramac–configurable custom computing
 Proceedings of IEEE Symposium on FPGAs for Custom Computing Machines
, 1995
"... can execute synchronous logic designs of up to one million gates at rates up to l megahertz. A fully configured Teramac includes half a gigabyte of RAM and hardware support for large multiported register files. The system has been built from custom FPGA's packaged in large multichip modules (MC ..."
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Cited by 42 (2 self)
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can execute synchronous logic designs of up to one million gates at rates up to l megahertz. A fully configured Teramac includes half a gigabyte of RAM and hardware support for large multiported register files. The system has been built from custom FPGA's packaged in large multichip modules (MCMs). A large custom circuit (1,000,000 gates) may be compiled onto the hardware in approximately 2 hours, without user intervention. The system is being used to explore the potential of custom computing machinery (CCM). 1 Teramac System Overview Research on special purpose parallel architectures and custom computing is very much an experimental science dependent on the existence of prototypes. We have built an FPGAbased configurable custom computing engine to enable experiments on an interesting scale. Teramac is a configurable hardware system comprising 1728 custom FPGAs and.5 gigabytes of RAM. It features: 1,000,000 gate capacity for synchronous logic circuits. up to 1 MHz clock rate..5 Gbytes of memory organized into 64 independent, 32bitwide banks, each with independent read and write ports. Banks may be combined horizontally and vertically to form large memories. Fully automatic compilation. Checkpoint restart capability. Scalability. A minimum Teramac system (a single board) supports designs of up to 64K gates. Additional boards may be added to expand the capacity incrementally, up to maximum of 16 boards. We are currently conducting experiments with an 8 board Teramac system. 2
Encapsulating Multiple CommunicationCost Metrics in Partitioning Sparse Rectangular Matrices for Parallel MatrixVector Multiplies
"... This paper addresses the problem of onedimensional partitioning of structurally unsymmetricsquare and rectangular sparse matrices for parallel matrixvector and matrixtransposevector multiplies. The objective is to minimize the communication cost while maintaining the balance on computational load ..."
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Cited by 41 (22 self)
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This paper addresses the problem of onedimensional partitioning of structurally unsymmetricsquare and rectangular sparse matrices for parallel matrixvector and matrixtransposevector multiplies. The objective is to minimize the communication cost while maintaining the balance on computational loads of processors. Most of the existing partitioning models consider only the total message volume hoping that minimizing this communicationcost metric is likely to reduce other metrics. However, the total message latency (startup time) may be more important than the total message volume. Furthermore, the maximum message volume and latency handled by a single processor are also important metrics. We propose a twophase approach that encapsulates all these four communicationcost metrics. The objective in the first phase is to minimize the total message volume while maintainingthe computationalload balance. The objective in the second phase is to encapsulate the remaining three communicationcost metrics. We propose communicationhypergraph and partitioning models for the second phase. We then present several methods for partitioning communication hypergraphs. Experiments on a wide range of test matrices show that the proposed approach yields very effective partitioning results. A parallel implementation on a PC cluster verifies that the theoretical improvements shown by partitioning results hold in practice.
A Hypergraph Framework For Optimal ModelBased Decomposition Of Design Problems
 Computational Optimization and Applications
, 1997
"... Decomposition of large engineering system models is desirable since increased model size reduces reliability and speed of numerical solution algorithms. The article presents a methodology for optimal modelbased decomposition (OMBD) of design problems, whether or not initially cast as optimization p ..."
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Cited by 35 (20 self)
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Decomposition of large engineering system models is desirable since increased model size reduces reliability and speed of numerical solution algorithms. The article presents a methodology for optimal modelbased decomposition (OMBD) of design problems, whether or not initially cast as optimization problems. The overall model is represented by a hypergraph and is optimally partitioned into weakly connected subgraphs that satisfy decomposition constraints. Spectral graphpartitioning methods together with iterative improvement techniques are proposed for hypergraph partitioning. A known spectral Kpartitioning formulation, which accounts for partition sizes and edge weights, is extended to graphs with also vertex weights. The OMBD formulation is robust enough to account for computational demands and resources and strength of interdependencies between the computational modules contained in the model. KEYWORDS: Model decomposition, multidisciplinary design, hypergraph partitioning, larges...
A General Framework for Vertex Orderings, with Applications to Netlist Clustering
, 1996
"... We present a general framework for the construction of vertex orderings for netlist clustering. Our WINDOW algorithm constructs an ordering by iteratively adding the vertex with highest attraction to the existing ordering. Variant choices for the attraction function allow our framework to subsume ma ..."
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Cited by 34 (12 self)
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We present a general framework for the construction of vertex orderings for netlist clustering. Our WINDOW algorithm constructs an ordering by iteratively adding the vertex with highest attraction to the existing ordering. Variant choices for the attraction function allow our framework to subsume many graph traversals and clustering objectives from the literature. The DPRP method of [3] is then applied to optimally split the ordering into a kway clustering. Our approach is adaptable to userspecified cluster size constraints. Experimental results for clustering and multiway partitioning are encouraging. 1 Introduction A netlist hypergraph H(V; E) consists of a set of modules (vertices) V = fv 1 ; v 2 ; : : : ; v n g and a set of nets (hyperedges) E = fe 1 ; e 2 ; : : : ; e m g. A cluster C i is a nonempty subset of V , and a kway clustering P k is a set of k clusters such that every v i 2 V belongs to exactly one cluster in P k . We study the following problem: The kWay Cl...