Optimal wire-sizing formula under the Elmore delay model

Chung-Ping Chen; Yao-Ping Chen; D. F. Wong

doi:10.1145/240518.240611

Optimal wire-sizing formula under the Elmore delay model

Chung-Ping Chen
, Yao-Ping Chen
, D. F. Wong

Office of the Provost

Research output: Chapter in book/report/conference proceeding › Chapter › peer-review

63 Citations (Scopus)

Abstract

In this paper, we consider non-uniform wire-sizing. Given a wire segment of length ℓ, let f(x) be the width of the wire at position x, 0≤x≤ℓ. We show that the optimal wire-sizing function that minimizes the Elmore delay through the wire is f(x) = ae^-bx, where a>0 and b>0 are constants that can be computed in O(1) time. In the case where lower bound (L>0) and upper bound (U>0) on the wire widths are given, we show that the optimal wire-sizing function f(x) is a truncated version of ae^-bx that can also be determined in O(1) time. Our wire-sizing formula can be iteratively applied to optimally size the wire segments in a routing tree.

Original language	English
Title of host publication	33rd ACM/IEEE Design Automation Conference - Proceedings 1996
Publisher	Association for Computing Machinery (ACM)
Pages	487-490
Number of pages	4
ISBN (Print)	9780897917797, 0780332946
DOIs	https://doi.org/10.1145/240518.240611 https://doi.org/10.1109/DAC.1996.545625
Publication status	Published - Jun 1996
Event	33rd ACM/IEEE Design Automation Conference, DAC 1996 - Las Vegas, United States Duration: 3 Jun 1996 → 7 Jun 1996 https://dl.acm.org/doi/proceedings/10.1145/240518 (Link to conference proceedings) https://ieeexplore.ieee.org/xpl/conhome/3826/proceeding

Publication series

Name	ACM/IEEE Design Automation Conference - Proceedings

Conference

Conference	33rd ACM/IEEE Design Automation Conference, DAC 1996
Country/Territory	United States
City	Las Vegas
Period	3/06/96 → 7/06/96
Internet address	https://dl.acm.org/doi/proceedings/10.1145/240518 (Link to conference proceedings) https://ieeexplore.ieee.org/xpl/conhome/3826/proceeding

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title = "Optimal wire-sizing formula under the Elmore delay model",

abstract = "In this paper, we consider non-uniform wire-sizing. Given a wire segment of length ℓ, let f(x) be the width of the wire at position x, 0≤x≤ℓ. We show that the optimal wire-sizing function that minimizes the Elmore delay through the wire is f(x) = ae-bx, where a>0 and b>0 are constants that can be computed in O(1) time. In the case where lower bound (L>0) and upper bound (U>0) on the wire widths are given, we show that the optimal wire-sizing function f(x) is a truncated version of ae-bx that can also be determined in O(1) time. Our wire-sizing formula can be iteratively applied to optimally size the wire segments in a routing tree.",

author = "Chung-Ping Chen and Yao-Ping Chen and Wong, \{D. F.\}",

note = "Funding Information: This work was partially supported by the Texas Advanced Research Program under Grant No.0036523459. Publisher Copyright: {\textcopyright} 1996 ACM; 33rd ACM/IEEE Design Automation Conference, DAC 1996 ; Conference date: 03-06-1996 Through 07-06-1996",

year = "1996",

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doi = "10.1145/240518.240611",

language = "English",

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series = "ACM/IEEE Design Automation Conference - Proceedings",

publisher = "Association for Computing Machinery (ACM)",

pages = "487--490",

booktitle = "33rd ACM/IEEE Design Automation Conference - Proceedings 1996",

address = "United States",

url = "https://dl.acm.org/doi/proceedings/10.1145/240518, https://ieeexplore.ieee.org/xpl/conhome/3826/proceeding",

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Chen, C-P, Chen, Y-P & Wong, DF 1996, Optimal wire-sizing formula under the Elmore delay model. in 33rd ACM/IEEE Design Automation Conference - Proceedings 1996. ACM/IEEE Design Automation Conference - Proceedings, Association for Computing Machinery (ACM), pp. 487-490, 33rd ACM/IEEE Design Automation Conference, DAC 1996, Las Vegas, Nevada, United States, 3/06/96. https://doi.org/10.1145/240518.240611, https://doi.org/10.1109/DAC.1996.545625

Optimal wire-sizing formula under the Elmore delay model. / Chen, Chung-Ping; Chen, Yao-Ping; Wong, D. F.
33rd ACM/IEEE Design Automation Conference - Proceedings 1996. Association for Computing Machinery (ACM), 1996. p. 487-490 (ACM/IEEE Design Automation Conference - Proceedings).

Research output: Chapter in book/report/conference proceeding › Chapter › peer-review

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N2 - In this paper, we consider non-uniform wire-sizing. Given a wire segment of length ℓ, let f(x) be the width of the wire at position x, 0≤x≤ℓ. We show that the optimal wire-sizing function that minimizes the Elmore delay through the wire is f(x) = ae-bx, where a>0 and b>0 are constants that can be computed in O(1) time. In the case where lower bound (L>0) and upper bound (U>0) on the wire widths are given, we show that the optimal wire-sizing function f(x) is a truncated version of ae-bx that can also be determined in O(1) time. Our wire-sizing formula can be iteratively applied to optimally size the wire segments in a routing tree.

AB - In this paper, we consider non-uniform wire-sizing. Given a wire segment of length ℓ, let f(x) be the width of the wire at position x, 0≤x≤ℓ. We show that the optimal wire-sizing function that minimizes the Elmore delay through the wire is f(x) = ae-bx, where a>0 and b>0 are constants that can be computed in O(1) time. In the case where lower bound (L>0) and upper bound (U>0) on the wire widths are given, we show that the optimal wire-sizing function f(x) is a truncated version of ae-bx that can also be determined in O(1) time. Our wire-sizing formula can be iteratively applied to optimally size the wire segments in a routing tree.

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ER -

Optimal wire-sizing formula under the Elmore delay model

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