### Abstract

This paper presents an algorithm for estimating, in the sense below, the length of a longest path of a given directed acyclic graph (DAG) whose edge lengths are given as random variables with normal distributions. Let F(x) be the distribution function of the length of a longest path of a given DAG. The algorithm computes a normal distribution function F̃(x) such that F̃(x) ≤ F(x) if F(x) ≥ α, given a constant α (0.5 ≤ α < 1.0). We conduct two experiments to demonstrate the accuracy of F̃(x).

Original language | English |
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Title of host publication | ACM/IEEE International Workshop on Timing Issues in the Specification and Synthesis of Digital Systems |

Publisher | Association for Computing Machinery (ACM) |

Pages | 134-139 |

Number of pages | 6 |

ISBN (Print) | 1581135262, 9781581135268 |

DOIs | |

Publication status | Published - 2002 |

Event | ACM/IEEE International Workshop on Timing Issues in the Specification and Synthesis of Digital Systems - Monterey, CA, United States Duration: Dec 2 2002 → Dec 3 2002 |

### Publication series

Name | ACM/IEEE International Workshop on Timing Issues in the Specification and Synthesis of Digital Systems |
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### Other

Other | ACM/IEEE International Workshop on Timing Issues in the Specification and Synthesis of Digital Systems |
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Country | United States |

City | Monterey, CA |

Period | 12/2/02 → 12/3/02 |

### All Science Journal Classification (ASJC) codes

- Engineering(all)

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## Cite this

Ando, E., Yamashita, M., Nakata, T., & Matsunaga, Y. (2002). The Statistical Longest Path Problem and its Application to Delay Analysis of Logical Circuits. In *ACM/IEEE International Workshop on Timing Issues in the Specification and Synthesis of Digital Systems*(pp. 134-139). (ACM/IEEE International Workshop on Timing Issues in the Specification and Synthesis of Digital Systems). Association for Computing Machinery (ACM). https://doi.org/10.1145/589411.589440