Results 1 - 10 of 5,476

New spectral methods for ratio cut partition and clustering

by Lars Hagen, Andrew B. Kahng - IEEE TRANS. ON COMPUTER-AIDED DESIGN , 1992
"... Partitioning 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 min-cut and equipartition, the two traditional goals of partitionin ..."
Abstract - Cited by 296 (17 self) - Add to MetaCart
Partitioning 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 min-cut and equipartition, the two traditional goals

Pin Balancing in Ratio Cut Partitioning

by Dirk Stroobandt - Proc. Swiss Conf. on CAD/CAM , 1999
"... Partitioning is a fundamental step in the computeraided design process. One of the best algorithms for partitioning is ratio cut [10] but, as many others, it does not take into account specific properties of multi-terminal nets, especially with regard to module pin count. In this paper, we show that ..."
Abstract - Cited by 1 (1 self) - Add to MetaCart
Partitioning is a fundamental step in the computeraided design process. One of the best algorithms for partitioning is ratio cut [10] but, as many others, it does not take into account specific properties of multi-terminal nets, especially with regard to module pin count. In this paper, we show

A Nondifferentiable Optimization Approach to Ratio-Cut Partitioning

by Karlis Freivalds
"... We propose a new method for finding the minimum ratio-cut of a graph. Ratio-cut is NP-hard problem for which the best previously known algorithm gives an O(log n)-factor approximation by solving its dually related maximum concurrent ow problem. We formulate the minimum ratio-cut as a certain nondiff ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
We propose a new method for finding the minimum ratio-cut of a graph. Ratio-cut is NP-hard problem for which the best previously known algorithm gives an O(log n)-factor approximation by solving its dually related maximum concurrent ow problem. We formulate the minimum ratio-cut as a certain

Spectral K-Way Ratio-Cut Partitioning Part I: Preliminary Results

by Pak K. Chan, Martine Schlag, Jason Zien
"... Recent research on partitioning has focussed on the ratio-cut cost metric which maintains a balance between the sizes of the edges cut and the sizes of the partitions without fixing the size of the partitions a priori. Iterative approaches and spectral approaches to two-way ratio-cut partitioning ha ..."
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Recent research on partitioning has focussed on the ratio-cut cost metric which maintains a balance between the sizes of the edges cut and the sizes of the partitions without fixing the size of the partitions a priori. Iterative approaches and spectral approaches to two-way ratio-cut partitioning

Pin Count Prediction In Ratio Cut Partitioning For VLSI And ULSI

by Dirk Stroobandt - Proc. IEEE Intl. Symp. on Circuits and Systems , 1999
"... Partitioning is an important step in computer-aided design. The `ratio cut' bipartitioning algorithm [1] is known to be one of the best partitioning algorithms. It partitions a circuit into two (disjoint) modules by cutting some of its nets. Based on theoretical arguments, the cost function tha ..."
Abstract - Cited by 7 (4 self) - Add to MetaCart
Partitioning is an important step in computer-aided design. The `ratio cut' bipartitioning algorithm [1] is known to be one of the best partitioning algorithms. It partitions a circuit into two (disjoint) modules by cutting some of its nets. Based on theoretical arguments, the cost function

Contour and Texture Analysis for Image Segmentation

by Jitendra Malik, Serge Belongie, Thomas Leung, Jianbo Shi , 2001
"... This paper provides an algorithm for partitioning grayscale images into disjoint regions of coherent brightness and texture. Natural images contain both textured and untextured regions, so the cues of contour and texture differences are exploited simultaneously. Contours are treated in the interveni ..."
Abstract - Cited by 404 (28 self) - Add to MetaCart
are to belong to the same region, we use the spectral graph theoretic framework of normalized cuts to find partitions of the image into regions of coherent texture and brightness. Experimental results on a wide range of images are shown.

Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms

by Tom Leighton, Satish Rao - J. ACM , 1999
"... In this paper, we establish max-flow min-cut theorems for several important classes of multicommodity flow problems. In particular, we show that for any n-node multicommodity flow problem with uniform demands, the max-flow for the problem is within an O(log n) factor of the upper bound implied by ..."
Abstract - Cited by 357 (6 self) - Add to MetaCart
to design the first polynomial-time (polylog n-times-optimal) approximation algorithms for well-known NP-hard optimization problems such as graph partitioning, min-cut linear arrangement, crossing number, VLSI layout, and minimum feedback arc set. Applications of the flow results to path routing problems

Multilevel hypergraph partitioning: Application in VLSI domain

by George Karypis, Rajat Aggarwal, Vipin Kumar, Shashi Shekhar - IEEE TRANS. VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS , 1999
"... In this paper, we present a new hypergraphpartitioning algorithm that is based on the multilevel paradigm. In the multilevel paradigm, a sequence of successively coarser hypergraphs is constructed. A bisection of the smallest hypergraph is computed and it is used to obtain a bisection of the origina ..."
Abstract - Cited by 315 (22 self) - Add to MetaCart
of the original hypergraph by successively projecting and refining the bisection to the next level finer hypergraph. We have developed new hypergraph coarsening strategies within the multilevel framework. We evaluate their performance both in terms of the size of the hyperedge cut on the bisection, as well

Expander Flows, Geometric Embeddings and Graph Partitioning

by Sanjeev Arora, Satish Rao, Umesh Vazirani - IN 36TH ANNUAL SYMPOSIUM ON THE THEORY OF COMPUTING , 2004
"... We give a O( log n)-approximation algorithm for sparsest cut, balanced separator, and graph conductance problems. This improves the O(log n)-approximation of Leighton and Rao (1988). We use a well-known semidefinite relaxation with triangle inequality constraints. Central to our analysis is a ..."
Abstract - Cited by 312 (18 self) - Add to MetaCart
We give a O( log n)-approximation algorithm for sparsest cut, balanced separator, and graph conductance problems. This improves the O(log n)-approximation of Leighton and Rao (1988). We use a well-known semidefinite relaxation with triangle inequality constraints. Central to our analysis is a

An optimal graph theoretic approach to data clustering: Theory and its application to image segmentation

by Zhenyu Wu, Richard Leahy - IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE , 1993
"... A novel graph theoretic approach for data clustering is presented and its application to the image segmentation problem is demonstrated. The data to be clustered are represented by an undirected adjacency graph G with arc capacities assigned to reflect the similarity between the linked vertices. Cl ..."
Abstract - Cited by 360 (0 self) - Add to MetaCart
. Clustering is achieved by removing arcs of G to form mutually exclusive subgraphs such that the largest inter-subgraph maximum flow is minimized. For graphs of moderate size (- 2000 vertices), the optimal solution is obtained through partitioning a flow and cut equivalent tree of 6, which can be efficiently
Results 1 - 10 of 5,476