## Congestion Driven Quadratic Placement (1998)

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Venue: | In Design Automation Conference |

Citations: | 30 - 1 self |

### BibTeX

@INPROCEEDINGS{Parakh98congestiondriven,

author = {Phiroze N. Parakh and Richard B. Brown and Karem A. Sakallah},

title = {Congestion Driven Quadratic Placement},

booktitle = {In Design Automation Conference},

year = {1998},

pages = {275--278},

publisher = {IEEE/ACM}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper introduces and demonstrates an extension to quadratic placement that accounts for wiring congestion. The algorithm uses an A * router and line-probe heuristics on region-based routing graphs to compute routing cost. The interplay between routing analysis and quadratic placement using a growth matrix permits global treatment of congestion. Further reduction in congestion is obtained by the relaxation of pin constraints. Experiments show improvements in wireability.

### Citations

203 | GORDIAN: VLSI Placement by Quadratic Programming and Slicing Optimization
- Kleinhans, Sigl, et al.
- 1991
(Show Context)
Citation Context ...on Conference ® Copyright ©1998 ACM 1-58113-049-x-98/0006/$3.50 DAC98 - 06/98 San Francisco, CA USAsFigure 1. First iteration of Quadratic placement 3. QUADRATIC PLACEMENT Quadratic placement engines =-=[7, 6, 9]-=- solve an unconstrained minimization problem, the objective function of which is the squared wirelength (1) where and are coordinate vectors for the cells and represents connectivity between cells . T... |

82 | Analytical Placement: A Linear or a Quadratic Objective Function
- Sigl, Doll, et al.
- 1991
(Show Context)
Citation Context ...on Conference ® Copyright ©1998 ACM 1-58113-049-x-98/0006/$3.50 DAC98 - 06/98 San Francisco, CA USAsFigure 1. First iteration of Quadratic placement 3. QUADRATIC PLACEMENT Quadratic placement engines =-=[7, 6, 9]-=- solve an unconstrained minimization problem, the objective function of which is the squared wirelength (1) where and are coordinate vectors for the cells and represents connectivity between cells . T... |

71 |
RISA: Accurate and Efficient Placement Routability Modeling
- Cheng
- 1994
(Show Context)
Citation Context ...rough a region, than are available. Therefore, schemes such as quadratic placement which are based solely on wire length minimization cannot adequately account for congestion. A simulated annealer in =-=[1]-=- used wire distribution functions and net bounding boxes for routingresource demand modeling. However, the complexity of its wire model precluded a global view and forced the analysis to be performed ... |

32 | A Timing-Driven Global Router for Custom Chip Design - Prasitjutrakul, Kubitz - 1990 |

28 |
Congestion-Driven Placement Using a New Multi-partitioning Heuristic
- Mayrhofer, Lauther
- 1990
(Show Context)
Citation Context ...demonstrated in [8] did account for some global routing resources, but did not address supply nor account for internal routing. Congestion-driven placement based on multi-partitioning was proposed in =-=[10]-=-, but was limited in the number of partitions due to the use of pre-computed Steiner trees. To our knowledge, congestion driven placement has not used congestion at a global level to update global pla... |

7 |
A Solution to Line-routing
- Hightower
- 1969
(Show Context)
Citation Context ...ation of the algorithm. The current implementation of the supply-demand algorithm creates global routes between regions using an A* search [2] algorithm and computes internal costs using a line-probe =-=[3]-=- heuristic. However, this component of the algorithm can be replaced with any appropriate route model. Further reductions in congestion, wire-length and area are obtained by the inclusion of relaxed p... |

4 |
Iterative Methods for Sparse Linear Systems
- Yousef
- 1996
(Show Context)
Citation Context ...he positive definite [7], and since is a diagonal matrix with positive diagonal entries, will have the same form as and thus (5) is a positive definite system. Standard SOR or Krylov subspace solvers =-=[12, 5]-=- can be used to solve the linear system. 1 – ( Z) T CZG 1 – ( )xi = – c' c' T ( Cx0+ dx) T G 1 – = Z Z C G G 1 – Z Z The use of G, causes cell positions to reflect supply-demand ratios. Resource limit... |

2 |
A fast clustering-based min-cut placement algorithm with simulated-annealing performance
- Saab
- 1996
(Show Context)
Citation Context ...ectives involve reducing net-cut costs or minimizing wire length. Due to their constructive nature, min-cut based strategies minimize the number of net crossings but fail to uniformly distribute them =-=[14]-=-. Quad-partitioning schemes, first demonstrated in [8] did account for some global routing resources, but did not address supply nor account for internal routing. Congestion-driven placement based on ... |

1 |
Boese et. al, “High-performance routing trees with identified critical sinks”. 30th DAC
- K
- 1993
(Show Context)
Citation Context ...rts increasingly accurate supply-demand modeling at each iteration of the algorithm. The current implementation of the supply-demand algorithm creates global routes between regions using an A* search =-=[2]-=- algorithm and computes internal costs using a line-probe [3] heuristic. However, this component of the algorithm can be replaced with any appropriate route model. Further reductions in congestion, wi... |

1 |
Meshach: Matrix Computations in C
- David
- 1994
(Show Context)
Citation Context ... C, was incorporated into an existing quadratic placer provided by Cascade Design Automation. The numerical routines for sparse matrix operations [12] were obtained through use of the Meshach library =-=[4]-=-. A subset of netlists from the ISCAS-89 benchmark (Table 1), were placed and subsequently analyzed. We express global flow uniformity as the average supply-demand excess over all edges, and local flo... |

1 |
Suaris et. al, “A quadrisection-based combined place and route scheme for standard cells
- R
- 1989
(Show Context)
Citation Context ...re length. Due to their constructive nature, min-cut based strategies minimize the number of net crossings but fail to uniformly distribute them [14]. Quad-partitioning schemes, first demonstrated in =-=[8]-=- did account for some global routing resources, but did not address supply nor account for internal routing. Congestion-driven placement based on multi-partitioning was proposed in [10], but was limit... |

1 |
Tsay et. al, “PROUD: A Fast sea-of-gates placement algorithm”. 25th DAC
- S
- 1988
(Show Context)
Citation Context ...on Conference ® Copyright ©1998 ACM 1-58113-049-x-98/0006/$3.50 DAC98 - 06/98 San Francisco, CA USAsFigure 1. First iteration of Quadratic placement 3. QUADRATIC PLACEMENT Quadratic placement engines =-=[7, 6, 9]-=- solve an unconstrained minimization problem, the objective function of which is the squared wirelength (1) where and are coordinate vectors for the cells and represents connectivity between cells . T... |

1 |
Performance-driven interconnect global routing
- Dongsheng
(Show Context)
Citation Context ...y. Further heuristics are then applied to manage local congestion to enhance and improve the final route quality. The concept of supply and demand to drive global routers is favorably demonstrated in =-=[13]-=-. The objective of this global router is defined in terms of route uniformity and route density. However, this scheme and others like it are unlikely to achieve optimality because the quality of a rou... |