Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc.

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Fast and high-quality document clustering algorithms play an important role in providing intuitive navigation and browsing mechanisms by organizing large amounts of information into a small number of meaningful clusters. In particular, hierarchical clustering solutions provide a view of the data at different levels of granularity, making them ideal for people to visualize and interactively explore large document collections.

An important application of graph partitioning is data clustering using a graph model | the pairwise similarities between all data objects form a weighted graph adjacency matrix that contains all necessary information for clustering. Here we propose a new algorithm for graph partition with an objective function that follows the min-max clustering principle. The relaxed version of the optimization of the min-max cut objective function leads to the Fiedler vector in spectral graph partition. Theoretical analyses of min-max cut indicate that it leads to balanced partitions, and lower bonds are derived. The min-max cut algorithm is tested on newsgroup datasets and is found to outperform other current popular partitioning/clustering methods. The linkagebased re nements in the algorithm further improve the quality of clustering substantially. We also demonstrate that the linearized search order based on linkage di erential is better than that based on the Fiedler vector, providing another e ective partition method.

this paper is organized as follows: Section 2 briefly describes the various ideas and algorithms implemented in METIS. Section 3 describes the user interface to the METIS graph partitioning and sparse matrix ordering packages. Sections 4 and 5 describe the formats of the input and output files used by METIS. Section 6 describes the stand-alone library that implements the various algorithms implemented in METIS. Section 7 describes the system requirements for the METIS package. Appendix A describes and compares various graph partitioning algorithms that are extensively used.

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Move-based iterative improvement partitioning methods such as the Fiduccia-Mattheyses (FM) algorithm [3] and Krishnamurthy's Look-Ahead (LA) algorithm [4] are widely used in VLSI CAD applications largely due to their time efficiency and ease of implementation. This class of algorithms is of the "local improvement" type. They generate relatively high quality results for small and medium size circuits. However, as VLSI circuits become larger, these algorithms are not so effective on them as direct partitioning tools. We propose new iterative-improvement methods that select cells to move with a view to moving clusters that straddle the two subsets of a partition into one of the subsets. The new algorithms significantly improve partition quality while preserving the advantage of time efficiency. Experimental results on 25 medium to large size ACM/SIGDA benchmark circuits show up to 70% improvement over FM in cutsize, with an average of per-circuit percent improvements of about 25%, and a t...

Iterative-improvement 2-way min-cut partitioning is an important phase in most circuit placement tools, and finds use in many other CAD applications. Most iterative improvement techniques for circuit netlists like the FiducciaMattheyses (FM) method compute the gains of nodes using local netlist information that is only concerned with the immediate improvement in the cutset. This can lead to misleading gain information. Krishnamurthy suggested a lookahead (LA) gain calculation method to ameliorate this situation; however, as we show, it leaves room for improvement. We present here a probabilistic gain computation approach called PROP (PRObabilistic Partitioner) that is capable of capturing the future implications of moving a node at the current time. We also propose an extended algorithm SHRINK-PROP that increases the probability of removing recently "perturbed" nets (nets whose nodes have been moved for the first time) from the cutset. This is necessary, since in a regular move process, the removal probabilities of most nets either remain unchanged or even decrease when their nodes are moved for the first time. Experimental results on medium- to large-size ACM/SIGDA benchmark circuits show that PROP and SHRINK-PROP outperform previous iterative-improvement methods like FM (by about 30% and 37%, respectively) and LA (by about 27% and 34%, respectively). Both PROP and SHRINK-PROP also obtain much better cutsizes than many recent state-of-the-art partitioners like EIG1, WINDOW, MELO, PARABOLI, GFM and GMetis (by 4.5% to 67%). We also show that the space and time complexities of PROP and SHRINK-PROP are very reasonable. Our empirical timing results reveal that PROP is appreciably faster than all recent techniques except GMetis---all other partitioners including ours work on...