### 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 |
---|---|

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 |

Publication status | Published - Jan 1 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 |
---|

### Other

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

Country | United States |

City | Monterey, CA |

Period | 12/2/02 → 12/3/02 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Engineering(all)

### Cite this

**The Statistical Longest Path Problem and its Application to Delay Analysis of Logical Circuits.** / Ando, Ei; Yamashita, Masafumi; Nakata, Toshio; Matsunaga, Yusuke.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*ACM/IEEE International Workshop on Timing Issues in the Specification and Synthesis of Digital Systems.*ACM/IEEE International Workshop on Timing Issues in the Specification and Synthesis of Digital Systems, Association for Computing Machinery (ACM), pp. 134-139, ACM/IEEE International Workshop on Timing Issues in the Specification and Synthesis of Digital Systems, Monterey, CA, United States, 12/2/02.

}

TY - GEN

T1 - The Statistical Longest Path Problem and its Application to Delay Analysis of Logical Circuits

AU - Ando, Ei

AU - Yamashita, Masafumi

AU - Nakata, Toshio

AU - Matsunaga, Yusuke

PY - 2002/1/1

Y1 - 2002/1/1

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=0141649415&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0141649415&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0141649415

SN - 1581135262

SN - 9781581135268

T3 - ACM/IEEE International Workshop on Timing Issues in the Specification and Synthesis of Digital Systems

SP - 134

EP - 139

BT - ACM/IEEE International Workshop on Timing Issues in the Specification and Synthesis of Digital Systems

PB - Association for Computing Machinery (ACM)

ER -