## Performance Driven Routing with Multiple Sources (1997)

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Venue: | In Proc. IEEE Int. Symp. on Circuits and Systems |

Citations: | 12 - 10 self |

### BibTeX

@INPROCEEDINGS{Cong97performancedriven,

author = {Jason Cong and Patrick H. Madden},

title = {Performance Driven Routing with Multiple Sources},

booktitle = {In Proc. IEEE Int. Symp. on Circuits and Systems},

year = {1997},

pages = {1--203}

}

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### Abstract

Existing routing problems for delay minimization consider the connection of a single source node to a number of sink nodes, with the objective of minimizing the delay from the source to all sinks, or a set of critical sinks. In this paper, we study the problem of routing nets with multiple sources, such as those found in signal busses. This new model assumes that each node in a net may be a source, a sink, or both. The objective is to optimize the routing topology to minimize the total weighted delay between all node pairs (or a subset of critical node pairs). We present a heuristic algorithm for the multiple-source performance-driven routing tree problem based on efficient construction of minimum-diameter minimum-cost Steiner trees. Experimental results on random nets with submicron CMOS IC and MCM technologies show an average of 12.6% and 21% reduction in the maximum interconnect delay, when compared with conventional minimum Steiner tree based topologies. Experimental results on mul...

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Citation Context ...es. Shortest path trees rooted at the source achieve this goal. A number of works address the radius objectives, both for general path length minimization, and also for skew minimization in clock nets=-=[13, 3, 6, 20]-=-. A minimum radius construction with a suitable root point may be also be a minimum diameter construction. When there are multiple sources and sinks, path length minimization can be achieved by minimi... |

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Citation Context ... a considerable effect on interconnect delay reduction when the resistance ratio is small. A number of optimized interconnect topologies have been proposed, including bounded-radius bounded-cost trees=-=[9]-=-, AHHK trees[1], LAST trees[21], maximum performance trees[7], A-trees[11], low-delay trees[5], and IDW/CFD trees[18]. These methods consider both the traditional concern of low total wire length, and... |

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Citation Context ...between a driver and sink can have comparable resistance to that of the transistor channel. Thus, changes to the interconnect length and topology can have a significant impact on delay. The result in =-=[11]-=- showed convincingly that interconnect topology optimization has a considerable effect on interconnect delay reduction when the resistance ratio is small. A number of optimized interconnect topologies... |

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Citation Context ...ll describe in section 3.3.4. The second step is to construct a shortest path tree rooted at r with low tree length. A rectilinear shortest path Steiner tree is also called a rectilinear arborescence =-=[22]-=-, or an A-Tree in short. Since the A-Tree algorithm[11] has proven to be very effective in generating a shortest path Steiner tree on the Manhattan plane with near minimum total wirelength, it is used... |

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Citation Context ...es. Shortest path trees rooted at the source achieve this goal. A number of works address the radius objectives, both for general path length minimization, and also for skew minimization in clock nets=-=[13, 3, 6, 20]-=-. A minimum radius construction with a suitable root point may be also be a minimum diameter construction. When there are multiple sources and sinks, path length minimization can be achieved by minimi... |

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Citation Context ... effect on interconnect delay reduction when the resistance ratio is small. A number of optimized interconnect topologies have been proposed, including bounded-radius bounded-cost trees[9], AHHK trees=-=[1]-=-, LAST trees[21], maximum performance trees[7], A-trees[11], low-delay trees[5], and IDW/CFD trees[18]. These methods consider both the traditional concern of low total wire length, and also the path ... |

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Citation Context ... nodes are shown in Table 1. Note that the second routing tree, which minimizes the maximum linear delay, does not fall entirely on the Hanan grid[16]. For the single source model under Elmore delay, =-=[4]-=- showed that an optimal tree which minimizes the maximum delay to any sink may not be contained by the Hanan grid, but also observed that these cases were rare. For problems with multiple sources, a s... |

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Citation Context ...he resistance ratio is small. A number of optimized interconnect topologies have been proposed, including bounded-radius bounded-cost trees[9], AHHK trees[1], LAST trees[21], maximum performance trees=-=[7]-=-, A-trees[11], low-delay trees[5], and IDW/CFD trees[18]. These methods consider both the traditional concern of low total wire length, and also the path length or Elmore delay between the source node... |

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Citation Context ...es. Shortest path trees rooted at the source achieve this goal. A number of works address the radius objectives, both for general path length minimization, and also for skew minimization in clock nets=-=[13, 3, 6, 20]-=-. A minimum radius construction with a suitable root point may be also be a minimum diameter construction. When there are multiple sources and sinks, path length minimization can be achieved by minimi... |

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Citation Context ...width and length, resulting in relatively constant transistor on resistance; the reduction in wire width on the other hand results in higher unit wire resistance [2]. As a result, the resistance ratio=-=[8]-=-, defined to be the driver resistance divided by the unit This work is partially supported by DARPA/ITO under Contract J-FBI-93-112, NSF Young Investigator Award MIP9357582, and a grant from Intel Cor... |

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Citation Context ...he construction of a tree at each point. The minimum length tree is selected as the final topology. 1-Steiner trees. To obtain a tree with low total length, the 1-Steiner algorithm of Kahng and Robins=-=[19]-=- is used. These trees place no bounds on path length, but have very good performance for tree length minimization. Note that existing performance driven interconnect optimization algorithms, listed in... |

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Citation Context ...tal tree cost, as measured by a combination of maximum path length, average path length, and total tree length. A number of results for minimum diameter trees on the Euclidean plane were presented in =-=[17]-=-. In particular, it was shown that the diameter of the smallest enclosing circle for a set of points also gives the minimum diameter for a tree connecting those points. After determination of this min... |