Combinatorial Algorithms for Integrated Circuit Layout

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Combinatorial Algorithms for Integrated Circuit Layout

07 Sep 1990-

TL;DR: This paper will concern you to try reading combinatorial algorithms for integrated circuit layout as one of the reading material to finish quickly.

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Abstract: Feel lonely? What about reading books? Book is one of the greatest friends to accompany while in your lonely time. When you have no friends and activities somewhere and sometimes, reading book can be a great choice. This is not only for spending the time, it will increase the knowledge. Of course the b=benefits to take will relate to what kind of book that you are reading. And now, we will concern you to try reading combinatorial algorithms for integrated circuit layout as one of the reading material to finish quickly.

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Journal Article•DOI•

Fast spectral methods for ratio cut partitioning and clustering

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L. Hagen¹, Andrew B. Kahng¹•Institutions (1)

University of California, Los Angeles¹

01 Jan 1991

TL;DR: It is shown that the second smallest eigenvalue of a matrix derived from the netlist gives a provably good approximation of the optimal ratio cut partition cost.

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Abstract: Partitioning of circuit netlists in VLSI design is considered. It is shown that the second smallest eigenvalue of a matrix derived from the netlist gives a provably good approximation of the optimal ratio cut partition cost. It is also demonstrated that fast Lanczos-type 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 by-product of the second eigenvector computation and are very successful on the difficult input classes proposed in the CAD literature. The intersection graph representation of the circuit netlist is considered, as a basis for partitioning, a heuristic based on spectral ratio cut partitioning of the netlist intersection graph is proposed. The partitioning heuristics were tested on industry benchmark suites, and the results were good in terms of both solution quality and runtime. Several types of algorithmic speedups and directions for future work are discussed. >

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1,282 citations

Journal Article•DOI•

Recent directions in netlist partitioning: a survey

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Charles J. Alpert¹, Andrew B. Kahng¹•Institutions (1)

University of California, Los Angeles¹

01 Aug 1995-Integration

TL;DR: This survey describes research directions in netlist partitioning during the past two decades in terms of both problem formulations and solution approaches, and discusses methods which combine clustering with existing algorithms (e.g., two-phase partitioning).

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673 citations

Cites background or methods from "Combinatorial Algorithms for Integr..."

...In addition, Lengauer [133] shows that no matter what weighting function is used, there exists a bipartitioning with deviation ( p jej) from the desired cost of cutting a single net....
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...Another formulation is the uniform multicommodity ow (UMCF) problem, which has been used to bipartition undirected edge-weighted graphs [138] [133]....
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...The book by Lengauer [133] is noteworthy, especially for its complete developmentof combinatorial algorithms (network ow, multicommodity ow, etc....
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...Further, they extend the average case bisection bound of Boppana [27] to k > 2 (see [133] for a more complete discussion of spectrally derived lower bounds)....
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...The book by Lengauer [133] is noteworthy, especially for its complete developmentof combinatorial algorithms (network ow, multicommodity ow, etc.)....
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Journal Article•DOI•

Fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems

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Stephen T. Barnard, Horst D. Simon

01 Apr 1994-Concurrency and Computation: Practice and Experience

TL;DR: In this paper, a multilevel version of RSB is introduced that attains about an order-of-magnitude improvement in run time on typical examples, and it is shown that RSB in its simplest form is expensive.

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Abstract: SUMMARY If problems involving unstructured meshes are to be solved efficiently on distributed-memory parallel computers, the meshes must be partitioned and distributed across processors in a way that balances the computational load and minimizes communication. The recursive spectral bisection method (RSB) has been shown to be very effective for such partitioning problems compared to alternative methods, but RSB in its simplest form is expensive. Here a multilevel version of RSB is introduced that attains about an order-of-magnitude improvement in run time on typical examples. 1. INTRODUCTION Unstructured meshes are used in several large-scale scientific and engineering problems, including finite-volume methods for computational fluid dynamics and finite-element methods for structural analysis. If unstructured problems such as these are to be solved on distributed-memory parallel computers, their data structures must be partitioned and distributed across processors; if they are to be solved efficiently, the partitioning must niaximize load balance and minimize interprocessor communication. Recently, the recursive spectral bisection method (RSB)[l] has been shown to be very effective for such partitioning problems compared to alternative methods. Unfortunately, RSB in its simplest form is expensive. We shall describe a multilevel version of RSB that attains about im order-of-magnitude improvement in run time on typical examples.

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567 citations

Journal Article•DOI•

Hypergraph-partitioning-based decomposition for parallel sparse-matrix vector multiplication

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Ümit V. Çatalyürek¹, Cevdet Aykanat¹•Institutions (1)

Bilkent University¹

01 Jul 1999-IEEE Transactions on Parallel and Distributed Systems

TL;DR: It is shown that the standard graph-partitioning-based decomposition of sparse matrices does not reflect the actual communication volume requirement for parallel matrix-vector multiplication, and two computational hypergraph models are proposed which avoid this crucial deficiency of the graph model.

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Abstract: In this work, we show that the standard graph-partitioning-based decomposition of sparse matrices does not reflect the actual communication volume requirement for parallel matrix-vector multiplication. We propose two computational hypergraph models which avoid this crucial deficiency of the graph model. The proposed models reduce the decomposition problem to the well-known hypergraph partitioning problem. The recently proposed successful multilevel framework is exploited to develop a multilevel hypergraph partitioning tool PaToH for the experimental verification of our proposed hypergraph models. Experimental results on a wide range of realistic sparse test matrices confirm the validity of the proposed hypergraph models. In the decomposition of the test matrices, the hypergraph models using PaToH and hMeTiS result in up to 63 percent less communication volume (30 to 38 percent less on the average) than the graph model using MeTiS, while PaToH is only 1.3-2.3 times slower than MeTiS on the average.

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560 citations

Cites background from "Combinatorial Algorithms for Integr..."

...The hypergraph partitioning problem is known to be NP-hard [29]....
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...In the standard clique-net model [29], a uniform cost of 1=siÿ1 is assigned to every clique edge of net ni with size si....
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...The graph partitioning problem is known to be NP-hard even for bipartitioning unweighted graphs [11]....
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...Hence, the hypergraph partitioning problem [29] can be defined as the task of dividing a hypergraph into two or more parts such that the cutsize is minimized while a given balance criterion (1) among the part weights is maintained....
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Proceedings Article•DOI•

Multilevel k-way hypergraph partitioning

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George Karypis¹, Vipin Kumar¹•Institutions (1)

University of Minnesota¹

01 Jun 1999

TL;DR: A new multilevel k-way hypergraph partitioning algorithm that substantially outperforms the existing state-of-the-art K-PM/LR algorithm for multi-way partitioning, both for optimizing local as well as global objectives.

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Abstract: In this paper, we present a new multilevel k-way hypergraph partitioning algorithm that substantially outperforms the existing state-of-the-art K-PM/LR algorithm for multi-way partitioning, both for optimizing local as well as global objectives. Experiments on the ISPD98 benchmark suite show that the partitionings produced by our scheme are on the average 15% to 23% better than those produced by the K-PM/LR algorithm, both in terms of the hyperedge cut as well as the (K-1) metric. Furthermore, our algorithm is significantly faster, requiring 4 to 5 times less time than that required by K-PM/LR.

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521 citations

Cites methods from "Combinatorial Algorithms for Integr..."

...This edge coarsening scheme is similar in nature to the schemes that treat the hypergraph as a graph by replacing each hyperedge with its clique representation [ 26 ]....
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Combinatorial Algorithms for Integrated Circuit Layout

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