## Abstract

In this paper, we determine the optimal shape function for a bi-directional wire under the Elmore delay model. Given a bi-directional wire of length L, let f(x) be the width of the wire at position x, 0≤x≤L. Let T_{DR} be the right-to-left delay. Let T_{DL} be the left-to-right delay. Let T_{BD} = αT_{DR}+βT_{DL} be the total weighted delay where α≥0 and β≥0 are given weights such that α+β = 1. We determine f(x) so that T_{BD} is minimized. Our study shows that, if α = β, the optimal shape function is f(x) = c, for some constant c; if α≠β, the optimal shape function can be expressed in terms of the Lambert's W function as f(x) = -c_{f}/2c_{0}(1/W(-ae^{-bx})+1), where c_{f} is the unit length fringing capacitance, c_{0} is the unit area capacitance, a and b are constants in terms of the given circuit parameters. If α = 0 or β = 0, our result gives the optimal shape function for a uni-directional wire.

Original language | English (US) |
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Pages (from-to) | 622-627 |

Number of pages | 6 |

Journal | IEEE/ACM International Conference on Computer-Aided Design, Digest of Technical Papers |

State | Published - 1997 |

Externally published | Yes |

Event | Proceedings of the 1997 IEEE/ACM International Conference on Computer-Aided Design, ICCAD - San Jose, CA, USA Duration: Nov 9 1997 → Nov 13 1997 |

## ASJC Scopus subject areas

- Software
- Computer Science Applications
- Computer Graphics and Computer-Aided Design