## Multilevel hypergraph partitioning: Application in VLSI domain (1999)

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Venue: | IEEE TRANS. VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS |

Citations: | 241 - 21 self |

### BibTeX

@INPROCEEDINGS{Karypis99multilevelhypergraph,

author = {George Karypis and Rajat Aggarwal and Vipin Kumar and Shashi Shekhar},

title = {Multilevel hypergraph partitioning: Application in VLSI domain},

booktitle = {IEEE TRANS. VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS},

year = {1999},

pages = {69--529},

publisher = {}

}

### Years of Citing Articles

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### Abstract

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 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 as on the run time for a number of very large scale integration circuits. Our experiments show that our multilevel hypergraph-partitioning algorithm produces high-quality partitioning in a relatively small amount of time. The quality of the partitionings produced by our scheme are on the average 6%–23 % better than those produced by other state-of-the-art schemes. Furthermore, our partitioning algorithm is significantly faster, often requiring 4–10 times less time than that required by the other schemes. Our multilevel hypergraph-partitioning algorithm scales very well for large hypergraphs. Hypergraphs with over 100 000 vertices can be bisected in a few minutes on today’s workstations. Also, on the large hypergraphs, our scheme outperforms other schemes (in hyperedge cut) quite consistently with larger margins (9%–30%).

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Citation Context ...ed by repeatedly moving vertices between the two parts to reduce the hyperedge-cut. These algorithms often use the Schweikert-Kernighan heuristic [2] (an extension of the Kernighan-Lin (KL) heuristic =-=[1]-=- for hypergraphs), or the faster Fiduccia-Mattheyses (FM) [3] refinement heuristic to iteratively improve the quality of the partition. In all of these methods (sometimes also called KLFM schemes), a ... |

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Citation Context ...than two vertices to be connected by a hyperedge. Formally, a hypergraph H = (V, Eh) is defined as a set of vertices V and a set of hyperedges Eh, where each hyperedge is a subset of the vertex set V =-=[29]-=-, and the size a hyperedge is the cardinality of this subset. *This work was supported by IBM Partnership Award, NSF CCR-9423082, Army Research Office contract DA/DAAH04-95-1-0538, and Army High Perfo... |

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Citation Context ...ning algorithm based upon this work, routinely finds substantially better bisections and is often two orders of magnitude faster than the hitherto state-of-the-art spectral-based bisection techniques =-=[6, 8]-=- for graphs. G GO O G G2 G G 1 G3 G2 G1 4 3 refined partitionprojected partition Coa rsen ingsPha se Initial Partitioning Phase Multilevel Graph Bisection Unc oar sen ingsandsRef inem entsPha se Figur... |

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Citation Context ...n the quality of the coarsening method. In many schemes, the projected partition is further improved using the FM refinement scheme [13]. Recently a new class of partitioning algorithms was developed =-=[10, 12, 11, 17]-=- that are based upon the multilevel paradigm. In these algorithms, a sequence of successively smaller (coarser) graphs is constructed. A bisection of the smallest graph is computed. This bisection is ... |

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Citation Context ...uce the hyperedge-cut. These algorithms often use the Schweikert-Kernighan heuristic [2] (an extension of the Kernighan-Lin (KL) heuristic [1] for hypergraphs), or the faster Fiduccia-Mattheyses (FM) =-=[3]-=- refinement heuristic to iteratively improve the quality of the partition. In all of these methods (sometimes also called KLFM schemes), a vertex is moved (or a vertex-pair is swapped) if it results i... |

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Citation Context ...s are visited in that order, and for each hyperedge that connects vertices that have not yet been matched, they are matched together. Thus, this scheme 1One can also compute a maximum weight matching =-=[32]-=-; however that would have significantly increased the amount of time required by this phase. 7sgives preference to the hyperedges that have large weight and those that are of small size. After all hyp... |

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Citation Context ... be better to move a vertex with smaller gain, as it may allow many good moves later. Second, if many vertices have the same gain, then the method offers no insight on which of these vertices to move =-=[4]-=-. Third, a hyperedge that has more than one vertices on both sides of the partition line does not influence the computation of the gain of vertices contained in it, making the gain computation quite i... |

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Citation Context ...troduction Hypergraph partitioning is an important problem and has extensive application to many areas, including VLSI design [16], efficient storage of large databases on disks [26], and data mining =-=[25]-=-. The problem is to partition the vertices of a hypergraph in k roughly equal parts, such that the number of hyperedges connecting vertices in different parts is minimized. A hypergraph is a generaliz... |

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Citation Context ...n the quality of the coarsening method. In many schemes, the projected partition is further improved using the FM refinement scheme [13]. Recently a new class of partitioning algorithms was developed =-=[10, 12, 11, 17]-=- that are based upon the multilevel paradigm. In these algorithms, a sequence of successively smaller (coarser) graphs is constructed. A bisection of the smallest graph is computed. This bisection is ... |

69 |
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Citation Context ...inite element grid partitioning, and by Hauck and Borriello [17] (called Optimized KLFM) and by Cong and Smith [11] for hypergraph partitioning. Karypis and Kumar extensively studied this paradigm in =-=[27, 33]-=- for partitioning of graphs. They presented new graph coarsening schemes for which even a good bisection of the coarsest graph is a pretty good bisection of the original graph. This makes the overall ... |

60 | A parellel bottom-up clustering algorithm with applications to circuit partitioning in VLSI design
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Citation Context ...uting fill-reducing matrix reordering, by Hendrickson and Leland [18] in the context of finiteelement mesh-partitioning, and by Hauck and Borriello (called Optimized KLFM) [20], and by Cong and Smith =-=[19]-=- for hypergraph partitioning. Karypis and Kumar extensively studied this paradigm in [21] and [22] for the partitioning of graphs. They presented new graph coarsening schemes for which even a good bis... |

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Citation Context ...se operations when disk access time is the bottleneck. By clustering related information we can minimize the number of disk accesses. Graph partitioning is an effective method for database clustering =-=[28]-=- but the performance can be further improved by using hypergraph partitioning. In particular, the database is modeled as hypergraph, in which the various items stored in the database (i.e., records) r... |

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Citation Context ...her research may identify better coarsening schemes that are suitable for a wider class of hypergraphs. New powerful variants of the FM refinement schemes have been developed recently by Dutt et al., =-=[22, 23]-=-. It will be instructive to include such a refinement scheme during the uncoarsening phase to see if it makes the multi-level scheme more robust. However, it is unclear if the added cost of these more... |

53 |
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Citation Context ...ten obtained randomly) and then the partition is refined by repeatedly moving vertices between the two parts to reduce the hyperedge-cut. These algorithms often use the Schweikert-Kernighan heuristic =-=[2]-=- (an extension of the Kernighan-Lin (KL) heuristic [1] for hypergraphs), or the faster Fiduccia-Mattheyses (FM) [3] refinement heuristic to iteratively improve the quality of the partition. In all of ... |

52 |
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Citation Context ...aph partitioning, multilevel algorithms. I. INTRODUCTION HYPERGRAPH partitioning is an important problem with extensive application to many areas, including very large scale integration (VLSI) design =-=[1]-=-, efficient storage of large databases on disks [2], and data mining [3]. The problem is to partition the vertices of a hypergraph into roughly equal parts, such that the number of hyperedges connecti... |

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Citation Context ...n the quality of the coarsening method. In many schemes, the projected partition is further improved using the FM refinement scheme [13]. Recently a new class of partitioning algorithms was developed =-=[10, 12, 11, 17]-=- that are based upon the multilevel paradigm. In these algorithms, a sequence of successively smaller (coarser) graphs is constructed. A bisection of the smallest graph is computed. This bisection is ... |

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Citation Context ...converted into a graph (by replacing each hyperedge by a set of regular edges), thenMETIS [21] can be used to compute a partitioning of this graph. This technique was investigated by Alpert and Khang =-=[25]-=- in their algorithm called GMetis. They converted hypergraphs to graphs by simply replacing each hyperedge with a clique, and then they dropped many edges from each clique randomly. They used METIS to... |

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Citation Context ...ion boundary. CDIP in conjunction with LA3 and CLIP in conjunction with PROP are two schemes that have shown the best results in their experiments. Another class of hypergraph partitioning algorithms =-=[5, 7, 13, 24]-=- performs partitioning in two phases. In the first phase, the hypergraph is coarsened to form a small hypergraph, and then the FM algorithm is used to bisect the small hypergraph. In the second phase,... |

43 | A new approach to effective circuit clustering
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Citation Context ...ion boundary. CDIP in conjunction with LA3 and CLIP in conjunction with PROP are two schemes that have shown the best results in their experiments. Another class of hypergraph partitioning algorithms =-=[5, 7, 13, 24]-=- performs partitioning in two phases. In the first phase, the hypergraph is coarsened to form a small hypergraph, and then the FM algorithm is used to bisect the small hypergraph. In the second phase,... |

41 | A probability-based approach to VLSI circuit partitioning
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Citation Context ..., a hyperedge that has more than one vertices on both sides of the partition line does not influence the computation of the gain of vertices contained in it, making the gain computation quite inexact =-=[22]-=-. Hence, these algorithms have been extended in a number of ways [4, 20, 22, 23]. Krishnamurthy [4] tried to introduce intelligence in the tie breaking process from among the many possible moves with ... |

35 | Partitioning Very Large Circuits Using Analytical Placement Techniques
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Citation Context ... obtained in a reasonable amount of time for a variety of benchmark problems. In particular, the performance of their resulting scheme is comparable to other state-of-the art schemes such as PARABOLI =-=[15]-=-, PROP [22], and the multilevel hypergraph partitioner from Hauck and Borriello [17]. The conversion of a hypergraph into a graph by replacing each hyperedge by a clique does not result in an equivale... |

35 | Partitioning similarity graphs: a framework for declustering problems
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(Show Context)
Citation Context ...gins (9% to 30%). 1 Introduction Hypergraph partitioning is an important problem and has extensive application to many areas, including VLSI design [16], efficient storage of large databases on disks =-=[26]-=-, and data mining [25]. The problem is to partition the vertices of a hypergraph in k roughly equal parts, such that the number of hyperedges connecting vertices in different parts is minimized. A hyp... |

34 | A general framework for vertex ordering with applications to netlist clustering
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(Show Context)
Citation Context ...ion boundary. CDIP in conjunction with LA3 and CLIP in conjunction with PROP are two schemes that have shown the best results in their experiments. Another class of hypergraph partitioning algorithms =-=[5, 7, 13, 24]-=- performs partitioning in two phases. In the first phase, the hypergraph is coarsened to form a small hypergraph, and then the FM algorithm is used to bisect the small hypergraph. In the second phase,... |

22 | A Simple Yet Effective Technique for Partitioning
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(Show Context)
Citation Context |

21 |
A fast and robust network bisection algorithm
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(Show Context)
Citation Context ...rtition line does not influence the computation of the gain of vertices contained in it, making the gain computation quite inexact [22]. Hence, these algorithms have been extended in a number of ways =-=[4, 20, 22, 23]-=-. Krishnamurthy [4] tried to introduce intelligence in the tie breaking process from among the many possible moves with the same high gain. He used a Look Ahead(LAr) algorithm which looks ahead up to ... |

20 |
ACM/SIGDA Design Automation Benchmarks: Catalyst or Anathema
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(Show Context)
Citation Context ...rmore, our partitioning algorithm is significantly faster, often requiring 4 to 10 times less time than that required by the other schemes. For many circuits in the well known ACM/SIGDA benchmark set =-=[9]-=-, our scheme is able to find better partitionings than those reported in the literature for any other hypergraph partitioning algorithm. 5sHG HGHG 1 2 HG3 HG HG 3HG 3HG 3HG HG3 HG 2HG Ref inem ent V-c... |

20 |
Modeling hypergraphs by graphs with the same mincut properties
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Citation Context ...l problem associated with replacing a hyperedge by its clique, is that there exists no scheme to assign weight to the edges of the clique that can correctly capture the cost of cutting this hyperedge =-=[14]-=-. This hinders the partitioning refinement algorithm since vertices are moved between partitions depending on the reduction in the number of edges they cut in the converted graph, whereas the real obj... |

16 |
Linear decomposition algorithm for VLSI design applications
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(Show Context)
Citation Context ...relatively small amount of time. The quality of the partitionings produced by our scheme are on the average 6%–23% better than those produced by other state-of-the-art schemes [11], [12], [25], [26], =-=[29]-=-. The difference in quality over other schemes becomes even greater for larger hypergraphs. Furthermore, our partitioning algorithm is significantly faster, often requiring 4–10 times less time than t... |

16 |
Computers and Instractability: A Guide to the Theory of NP-Completeness
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(Show Context)
Citation Context ...ph-partitioning algorithm greatly affects the feasibility, quality, and cost of the resulting system. A. Related Work The problem of computing an optimal bisection of a hypergraph is at least NP-hard =-=[5]-=-. However, because of the importance of the problem in many application areas, many heuristic algorithms have been developed. The survey by Alpert and Khang [1] provides a detailed description and com... |

8 |
METIS 3.0: Unstructured graph partitioning and sparse matrix ordering system
- Karypis, Kumar
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(Show Context)
Citation Context ...inite element grid partitioning, and by Hauck and Borriello [17] (called Optimized KLFM) and by Cong and Smith [11] for hypergraph partitioning. Karypis and Kumar extensively studied this paradigm in =-=[27, 33]-=- for partitioning of graphs. They presented new graph coarsening schemes for which even a good bisection of the coarsest graph is a pretty good bisection of the original graph. This makes the overall ... |

4 | circuit partitioning by cluster-removal using iterative improvement techniques - “VLSI - 1996 |

2 |
Combinatorial Optimization: Networks and Matroids
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(Show Context)
Citation Context ...is is illustrated in Figure 3. Figure 3(a) shows the original hyperedge and Figure 3(b) shows the graph obtained after replacing the hyperedge by its clique. The standard hyperedge to edge conversion =-=[31]-=- assigns a uniform weight of 1/(|e| - 1) to each edge in the clique, where |e| is the size of the hyperegde i.e., the number of vertices in the hyperedge. Thus, in our example, each edge is assigned a... |

2 |
Computers and Instractability: A Guide to the Theory
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(Show Context)
Citation Context ...ations and declustering data in parallel databases [26]. 2 1/3 1 f D 1/3 E (c) G 5/6 4/3 1/2 F 3/2 Gs1.1 Related Work The problem of computing an optimal bisection of a hypergraph is at least NP-hard =-=[30]-=-. However, because of the importance of the problem in many application areas, many heuristic algorithms have been developed. The survey by Alpert and Khang [16] provides a detailed description and co... |