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## Multilevel Circuit Partitioning (1998)

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Venue: | IN PROC. OF THE 34TH ACM/IEEE DESIGN AUTOMATION CONFERENCE |

Citations: | 89 - 8 self |

### Citations

1342 |
An efficient heuristic procedure for partitioning graphs
- Kernighan, Lin
- 1970
(Show Context)
Citation Context ...t Given a balance tolerance the min-cut bipartitioning problem seeks a solution that minimizes subject to The standard bipartitioning approach is iterative improvement based on the Kernighan–Lin (KL) =-=[29]-=- algorithm, which was later improved by Fiduccia–Mattheyses (FM) [15]. The FM algorithm proceeds in a series of passes. A pass begins Manuscript received May 2, 1997. This work was supported by a gran... |

523 |
A multi-level algorithm for partitioning graphs,”
- Hendrickson, Leland
- 1995
(Show Context)
Citation Context ...arious levels. The result is an efficient partitioner that produces the lowest cost solutions in the literature. Fig. 2 describes ML, our new multilevel algorithm (which follows the same structure as =-=[22]-=-) for partitioning netlist hypergraphs. The algorithm accepts a netlist as input along with two user parameters and specifies that coarsening should proceed as long as the number of modules in the cur... |

350 |
A linear time heuristic for improving network partitions,” in
- Fiduccia, Mattheyses
- 1982
(Show Context)
Citation Context ...a solution that minimizes subject to The standard bipartitioning approach is iterative improvement based on the Kernighan–Lin (KL) [29] algorithm, which was later improved by Fiduccia–Mattheyses (FM) =-=[15]-=-. The FM algorithm proceeds in a series of passes. A pass begins Manuscript received May 2, 1997. This work was supported by a grant from Cadence Design Systems, Inc. This paper was recommended by Ass... |

307 | A fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems
- Barnard, Simon
- 1992
(Show Context)
Citation Context ... the same time find a good final solution via refinement at the low levels. Multilevel partitioning approaches have been especially prominent in the scientific computing literature. Barnard and Simon =-=[6]-=- have used multilevel techniques not directly for partitioning, but rather to compute the Fiedler vector for spectral bisection. Inspired by this work, Hendrickson and Leland [22] developed a very eff... |

292 | New spectral methods for ratio cut partitioning and clustering - Hagen, Kahng - 2002 |

225 | GORDIAN: VLSI Placement by Quadratic Programming and Slicing Optimization."
- Kleinhans, Sigl, et al.
- 1991
(Show Context)
Citation Context ...mpared to previous algorithms while requiring a reasonable amount of CPU resources. D. Quadrisection Comparisons Our final set of experiments compares ML for four-way partitioning against the GORDIAN =-=[30]-=- standard cell placement program. In GORDIAN, the I/O pads are initially preplaced, then a system of equations is solved to find the locations of the unfixed modules such that either a squared wire-le... |

219 | Recent directions in netlist partitioning: a survey, Integration: The VLSI
- Alpert, Kahng
- 1995
(Show Context)
Citation Context ...ith directions for future work. II. INNOVATIONS IN ITERATIVE PARTITIONING We now review selected works in iterative partitioning which have provided new innovation (see the survey of Alpert and Kahng =-=[2]-=- for a broader view of previous work in partitioning). In our discussion of the algorithms below, we include some comparisons of these methods (using our implementations) for 23 of the standard benchm... |

140 |
Multiple-Way Network Partitioning."
- Sanchis
- 1989
(Show Context)
Citation Context ...the same gain; hence, various tie-breaking strategies have been proposed to choose among alternate moves that have the same gain. Krishnamurthy [31] proposed using lookahead gain vectors, and Sanchis =-=[39]-=- extended this approach to multiway partitioning. Even when gain vectors are used, ties may still occur in the first- through th-level gains. Thus, it is the implementation of the gain bucket data str... |

123 |
An Improved Min-Cut Algorithm for Partitioning VLSI Networks,"
- Krishnamurthy
- 1984
(Show Context)
Citation Context ... it better via small changes), easy to describe and implement, and relatively fast. Hence, much work has sought to improve upon the basic FM algorithm by introducing module tie-breaking schemes [19], =-=[31]-=-, by modifying the module locking and unlocking mechanism [11], [23], or by using different formulas for computing the gain [13], [14]. Other works attempt to use iterative improvement inside other al... |

80 |
A heuristic for reducing fill in sparse matrix factorization”,
- Bui, Jones
- 1993
(Show Context)
Citation Context ...son and Leland [22] developed a very efficient multilevel partitioning algorithm which is included in the Chaco partitioning package. The coarsening step finds a random maximal matching as in [7] and =-=[8]-=-, and merges pairs of modules to reduce the instance size by a factor of 2. The refinement step uses multiway FM with a LIFO bucket scheme, but with several modifications to improve run times: 1) the ... |

67 | A Parallel Bottom-up Clustering Algorithm with Applications to Circuit Partitioning in VLSI Design.
- Cong, Smith
- 1993
(Show Context)
Citation Context ...rovement inside other algorithmic approaches such as genetic algorithms [9], tabu search [5], large-scale Markov chains [16], two-phase clustering [7], [17], [33], [40], or multilevel clustering [3], =-=[10]-=-, [22], [21], [27]. This paper proposes a new multilevel circuit partitioning algorithm. Our work is motivated by the multilevel partitioners of Hendrickson and Leland [22] and Karypis and Kumar [27] ... |

61 | An evaluation of bipartitioning technique. In:
- Hauck, Borriello
- 1995
(Show Context)
Citation Context ...ide other algorithmic approaches such as genetic algorithms [9], tabu search [5], large-scale Markov chains [16], two-phase clustering [7], [17], [33], [40], or multilevel clustering [3], [10], [22], =-=[21]-=-, [27]. This paper proposes a new multilevel circuit partitioning algorithm. Our work is motivated by the multilevel partitioners of Hendrickson and Leland [22] and Karypis and Kumar [27] which have b... |

61 | VLSI Circuit Partitioning by Cluster-Removal Using Iterative Improvement and TimberWolf7.0. Techniques." - Dutt, Deng - 1996 |

52 | Partitioning-based Standard-cell Global Placement with an Exact Objective".
- Huang, Kahng
- 1997
(Show Context)
Citation Context ...section, i.e., four-way partitioning. We use the quadrisection algorithm of Sanchis [39], but without lookahead. We have implemented the sum of cluster degrees, net cut, and generic gain computations =-=[24]-=-; our quadrisection results are reported for the sum of degrees gain computation. To utilize our quadrisection algorithm within a placement tool, the user can preassign some modules (e.g., I/O pads) t... |

50 | A new approach to effective circuit clustering.
- Hagen, Kahng
- 1992
(Show Context)
Citation Context ..., [14]. Other works attempt to use iterative improvement inside other algorithmic approaches such as genetic algorithms [9], tabu search [5], large-scale Markov chains [16], two-phase clustering [7], =-=[17]-=-, [33], [40], or multilevel clustering [3], [10], [22], [21], [27]. This paper proposes a new multilevel circuit partitioning algorithm. Our work is motivated by the multilevel partitioners of Hendric... |

47 |
Improving the performance of the Kernighan-Lin and simulated annealing graph bisection algorithms
- Bui, Heigham, et al.
- 1989
(Show Context)
Citation Context ... [13], [14]. Other works attempt to use iterative improvement inside other algorithmic approaches such as genetic algorithms [9], tabu search [5], large-scale Markov chains [16], two-phase clustering =-=[7]-=-, [17], [33], [40], or multilevel clustering [3], [10], [22], [21], [27]. This paper proposes a new multilevel circuit partitioning algorithm. Our work is motivated by the multilevel partitioners of H... |

45 | A Hybrid Multilevel/Genetic Approach for Circuit Partitioning." In
- Alpert, Hagen, et al.
- 1996
(Show Context)
Citation Context ...cheme, the initial partitioning algorithm, and the refinement scheme. One of their coarsening schemes uses a greedy weighted matching algorithm, upon which our coarsening scheme is based. The work of =-=[1]-=- adapted Metis to partition netlist hypergraphs while integrating the genetic approach of [20] to obtain more stable solution quality. Cong and Smith [10] proposed applying their clique finding cluste... |

44 | A Probability-Based Approach to VLSI Circuit Partitioning,”
- Dutt, Deng
- 1996
(Show Context)
Citation Context ...the basic FM algorithm by introducing module tie-breaking schemes [19], [31], by modifying the module locking and unlocking mechanism [11], [23], or by using different formulas for computing the gain =-=[13]-=-, [14]. Other works attempt to use iterative improvement inside other algorithmic approaches such as genetic algorithms [9], tabu search [5], large-scale Markov chains [16], two-phase clustering [7], ... |

43 | Multilevel graph partitioning schemes, in:
- Karypis, Kumar
- 1995
(Show Context)
Citation Context ...her algorithmic approaches such as genetic algorithms [9], tabu search [5], large-scale Markov chains [16], two-phase clustering [7], [17], [33], [40], or multilevel clustering [3], [10], [22], [21], =-=[27]-=-. This paper proposes a new multilevel circuit partitioning algorithm. Our work is motivated by the multilevel partitioners of Hendrickson and Leland [22] and Karypis and Kumar [27] which have been ve... |

42 | Partitioning very large circuits using analytical placement techniques”,
- Riess, Doll, et al.
- 1994
(Show Context)
Citation Context ...eas. They report results for ten runs of HB, and show that it outperforms the flowbased algorithm of Yang and Wong [42] and spectral bipartitioning [18]. • The PARABOLI (PB) algorithm of Riess et al. =-=[36]-=- was widely considered to be the state-of-the-art partitioner in 1994, and has been the subject of numerous comparisons since [21], [42], [32], [14], [13]. The authors of [36] report cuts that are 50%... |

36 | A General Framework For Vertex Orderings, With Applications to Netlist Clustering". - Alpert, Hagen, et al. - 1996 |

31 | On Implementation Choices for Iterative Improvement Partitioning Algorithms." In
- Hagen, Huang, et al.
- 1995
(Show Context)
Citation Context ...y make it better via small changes), easy to describe and implement, and relatively fast. Hence, much work has sought to improve upon the basic FM algorithm by introducing module tie-breaking schemes =-=[19]-=-, [31], by modifying the module locking and unlocking mechanism [11], [23], or by using different formulas for computing the gain [13], [14]. Other works attempt to use iterative improvement inside ot... |

31 |
Ecient Network Flow Based Min-Cut Balanced Partitioning
- Yang, Wong
- 1994
(Show Context)
Citation Context ...ting bipartitionings still fall within the required size constraints even for unit areas. They report results for ten runs of HB, and show that it outperforms the flowbased algorithm of Yang and Wong =-=[42]-=- and spectral bipartitioning [18]. • The PARABOLI (PB) algorithm of Riess et al. [36] was widely considered to be the state-of-the-art partitioner in 1994, and has been the subject of numerous compari... |

23 | A Simple Yet Effective Technique for Partitioning
- Shin, Kim
- 1993
(Show Context)
Citation Context ...r works attempt to use iterative improvement inside other algorithmic approaches such as genetic algorithms [9], tabu search [5], large-scale Markov chains [16], two-phase clustering [7], [17], [33], =-=[40]-=-, or multilevel clustering [3], [10], [22], [21], [27]. This paper proposes a new multilevel circuit partitioning algorithm. Our work is motivated by the multilevel partitioners of Hendrickson and Lel... |

23 |
Analytical Placement: A Linear or a Quadratic Objeclive Function
- Johannes
- 1991
(Show Context)
Citation Context ..., the I/O pads are initially preplaced, then a system of equations is solved to find the locations of the unfixed modules such that either a squared wire-length [30] or a linear wire-length objective =-=[41]-=- (GORDIAN-L) is optimized. The solution to this system induces an ordering of the modules in the horizontal direction which is then split into a bipartitioning. 3 Then, another optimization induces a ... |

21 |
A fast and robust network bisection algorithm
- Saab
- 1995
(Show Context)
Citation Context ... increase by a factor of 4–8. The heuristic is nevertheless still fairly efficient, and future work on probabilistic gain computations is certainly promising. B. Modifying the Basic FM Structure Saab =-=[38]-=- observes that in an iterative improvement algorithm, when a vertex is moved, it tends to “drag” with it itssALPERT et al.: MULTILEVEL CIRCUIT PARTITIONING 657 TABLE II MINIMUM CUT, AVERAGE CUT, AND S... |

19 | Combining problem reduction and adaptive multistart: A new technique for superior iterative partitioning
- Hagen, Kahng
- 1997
(Show Context)
Citation Context ...hwhile remains an open direction for future work. C. Using an Iterative Improvement Engine As problem sizes grow larger, the performance of iterative improvement approaches such as FM tend to degrade =-=[20]-=-. Hence, many heuristics have utilized iterative improvement within a different paradigm. For example, the genetic partitioning algorithm of Bui and Moon [9] uses FM as a postprocessing step to each c... |

19 |
Improvements of a mincut partition algorithm.
- Ng, eld, et al.
- 1987
(Show Context)
Citation Context .... Other works attempt to use iterative improvement inside other algorithmic approaches such as genetic algorithms [9], tabu search [5], large-scale Markov chains [16], two-phase clustering [7], [17], =-=[33]-=-, [40], or multilevel clustering [3], [10], [22], [21], [27]. This paper proposes a new multilevel circuit partitioning algorithm. Our work is motivated by the multilevel partitioners of Hendrickson a... |

17 | Advanced search techniques for circuit partitioning
- Areibi, Vannelli
- 1993
(Show Context)
Citation Context ... Bui and Moon [9] uses FM as a postprocessing step to each crossover operation. (A similar approach was proposed by [25].) FM postprocessing has also been utilized within tabu search-based approaches =-=[4]-=-, [5]. Fukunaga et al. [16] proposed a large-step Markov Chain (LSMC) algorithm which generates new solutions by making big “jumps” from low-cost local minima. These solutions are then used as startin... |

15 | Linear decomposition algorithm for VLSI design applications - Li, Lillis, et al. - 1995 |

12 |
A Fast and Stable Hybrid Genetic Algorithm for the Ratio-Cut Partitioning
- Bui, Moon
- 1994
(Show Context)
Citation Context ...mechanism [11], [23], or by using different formulas for computing the gain [13], [14]. Other works attempt to use iterative improvement inside other algorithmic approaches such as genetic algorithms =-=[9]-=-, tabu search [5], large-scale Markov chains [16], two-phase clustering [7], [17], [33], [40], or multilevel clustering [3], [10], [22], [21], [27]. This paper proposes a new multilevel circuit partit... |

11 | Multi-way Graph and Hypergraph Partitioning. - Alpert - 1996 |

8 |
The weighted graph bi-partitioning problem: A look at ga performance
- Inayoshi, Manderick
- 1994
(Show Context)
Citation Context ...ment within a different paradigm. For example, the genetic partitioning algorithm of Bui and Moon [9] uses FM as a postprocessing step to each crossover operation. (A similar approach was proposed by =-=[25]-=-.) FM postprocessing has also been utilized within tabu search-based approaches [4], [5]. Fukunaga et al. [16] proposed a large-step Markov Chain (LSMC) algorithm which generates new solutions by maki... |

7 | A gradient method on the initial partition of FiducciaMattheyses algorithm
- Liu, Kuo, et al.
- 1993
(Show Context)
Citation Context ...rates new solutions by making big “jumps” from low-cost local minima. These solutions are then used as starting solutions in FM to generate new local minima (also see Isomoto et al. [26]). Liu et al. =-=[32]-=- proposed a gradient Fiduccia–Mattheyses algorithm (GFM) that alternates FM refinements with gradient descents. They also propose a variant (GFM which uses the two-phase FM technique described below. ... |

7 |
An efficient algorithm for VLSI network partitioning problem using a cost function with balancing factor
- Park, Park
- 1993
(Show Context)
Citation Context ...or dual passes are a factor of 9–10 higher than for a primal pass. In their study on circuit partitioning algorithms, the authors of [21] conclude that dual passes “are not worthwhile.” Park and Park =-=[34]-=- propose to integrate size constraints into the cut objective, and Shin and Kim [40] propose to gradually tighten size constraints between FM passes. These are just some of the many proposed modificat... |

6 |
Graph contraction for mapping data on parallel computers: A quality-cost tradeoff
- Ponnusamy, Mansour, et al.
- 1994
(Show Context)
Citation Context ...oundary refinement scheme is used wherein only vertices incident to cut edges are inserted into the data structure, with gains for other vertices computed only on an “as needed” basis. The authors of =-=[35]-=- also proposed a multilevel algorithm but without refinement, i.e., a partition of the coarsest graph is uncoarsened in one step to form the final solution. Karypis and Kumar [27], [28] recently devel... |

6 | A new approach to e ective circuit clustering - Hagen, Kahng - 1992 |

5 |
Improved multiple-way circuit partitioning algorithms
- Dasdan, Aykanat
- 1994
(Show Context)
Citation Context ... and relatively fast. Hence, much work has sought to improve upon the basic FM algorithm by introducing module tie-breaking schemes [19], [31], by modifying the module locking and unlocking mechanism =-=[11]-=-, [23], or by using different formulas for computing the gain [13], [14]. Other works attempt to use iterative improvement inside other algorithmic approaches such as genetic algorithms [9], tabu sear... |

5 | A GRASP clustering technique for circuit partitioning,” in Satisfiability problems - Areibi, Vannelli - 1997 |

5 | An Efficient Clustering Technique for Circuit Partitioning - Areibi, Vannelli - 1996 |

5 | Linear Decomposition Algorithm for - Li, Lillis, et al. - 1995 |

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

4 |
A probabilistic multi-commodity flow solution to circuit clustering problems
- Yeh, Cheng, et al.
- 1992
(Show Context)
Citation Context ...etis. In addition, a matchingbased approach allows us to control the total number of levels in the netlist hierarchy (as opposed to other approaches, e.g., random walks [17], shortest path clustering =-=[43]-=-, and clique compression [10], which automatically determine the number of clusters). The Match algorithm starts by randomly permuting the module indexes, and then visits each module in turn. A permut... |

3 |
spectral methods for ratio cut partitioning and clustering
- New
- 1992
(Show Context)
Citation Context ...ithin the required size constraints even for unit areas. They report results for ten runs of HB, and show that it outperforms the flowbased algorithm of Yang and Wong [42] and spectral bipartitioning =-=[18]-=-. • The PARABOLI (PB) algorithm of Riess et al. [36] was widely considered to be the state-of-the-art partitioner in 1994, and has been the subject of numerous comparisons since [21], [42], [32], [14]... |

3 | The dynamic locking heuristic { a new graph partitioning algorithm - man - 1994 |

2 |
general framework for vertex orderings, with applications to circuit clusterings
- “A
- 1994
(Show Context)
Citation Context ...e improvement inside other algorithmic approaches such as genetic algorithms [9], tabu search [5], large-scale Markov chains [16], two-phase clustering [7], [17], [33], [40], or multilevel clustering =-=[3]-=-, [10], [22], [21], [27]. This paper proposes a new multilevel circuit partitioning algorithm. Our work is motivated by the multilevel partitioners of Hendrickson and Leland [22] and Karypis and Kumar... |

2 |
efficient clustering technique for circuit partitioning
- “An
- 1996
(Show Context)
Citation Context ...23], or by using different formulas for computing the gain [13], [14]. Other works attempt to use iterative improvement inside other algorithmic approaches such as genetic algorithms [9], tabu search =-=[5]-=-, large-scale Markov chains [16], two-phase clustering [7], [17], [33], [40], or multilevel clustering [3], [10], [22], [21], [27]. This paper proposes a new multilevel circuit partitioning algorithm.... |

2 | Iterative improvement by network flow methods - Doll, Johannes, et al. - 1994 |

2 | multilevel graph partitioning, - Parallel - 1995 |

1 | Large-Step Markov Chain Variants for VLSI Netlist Partitioning
- Fukunaga, Huang, et al.
- 1996
(Show Context)
Citation Context ...ulas for computing the gain [13], [14]. Other works attempt to use iterative improvement inside other algorithmic approaches such as genetic algorithms [9], tabu search [5], large-scale Markov chains =-=[16]-=-, two-phase clustering [7], [17], [33], [40], or multilevel clustering [3], [10], [22], [21], [27]. This paper proposes a new multilevel circuit partitioning algorithm. Our work is motivated by the mu... |

1 | The dynamic locking heuristic–A new graph partitioning algorithm - Hoffman - 1994 |

1 |
A graph bisection algorithms based on subgraph migration
- Isomoto, Mimasa, et al.
- 1994
(Show Context)
Citation Context ...gorithm which generates new solutions by making big “jumps” from low-cost local minima. These solutions are then used as starting solutions in FM to generate new local minima (also see Isomoto et al. =-=[26]-=-). Liu et al. [32] proposed a gradient Fiduccia–Mattheyses algorithm (GFM) that alternates FM refinements with gradient descents. They also propose a variant (GFM which uses the two-phase FM technique... |

1 |
general purpose, multiple-way partitioning algorithm
- “A
- 1994
(Show Context)
Citation Context ...hm to reverse a sequence of bad moves, and then try some different sequence. Backing up in this manner prevents continuing an entire pass in which positive gain is unlikely to be realized. Yeh et al. =-=[44]-=- proposed an extension of Sanchis’ multiway partitioning algorithm that alternates “primal” passes of module moves with “dual” passes of net moves; however, run times for dual passes are a factor of 9... |

1 | MLC GMet HB PB GFM GFMt CL- CD- CL- LSMC Case (100) (10) LA3f LA3f PRf balu 27 - MLC - 1996 |

1 | Iterative Improvement byNetwork Flow Methods - Doll, Johannes, et al. - 1994 |

1 | A Probability-Based Approach toVLSI Circuit Partitioning - Dutt, Deng - 1996 |

1 | On Implementation Choices for IterativeImprovementPartitioning Algorithms - Hagen, Huang, et al. - 1995 |

1 | Kahng "Partitioning-Based StandardCell Global Placement with An Exact Objective - Huang, B - 1997 |

1 | MLC GMet HB PB GFM GFM t CL- CD- CL- LSMC Case (100) (10) LA3 f LA3 f PR f balu 27 27 27 41 27 28 27 27 27 27 bm1 47 51 48 51 47 47 49 primary1 47 52 47 53 47 51 51 47 51 49 test04 48 49 49 49 48 52 69 test03 56 58 62 56 57 57 63 test02 89 92 95 91 89 87 - MLC |

1 | The DynamicLocking Heuristic -- A New Graph Partitioning Algorithm - Hoffman - 1994 |

1 | A Probability-Based Approach to - Dutt, Deng - 1996 |