## Abstract

Graph algorithms are widely used in VLSI CAD. Traditional graph algorithms can handle graphs with deterministic edge weights. As VLSI technology continues to scale into nanometer designs, we need to use probability distributions for edge weights in order to model uncertainty due to parameter variations. In this paper, we consider the statistical shortest path (SSP) problem. Given a graph G, the edge weights of G are random variables. For each path P in G, let L _{P} be its length, which is the sum of all edge weights on P. Clearly L_{P} is a random variable and we let μ_{P} and σ_{P}^{2} be its mean and variance, respectively. In the SSP problem, our goal is to find a path P connecting two given vertices to minimize the cost function μ_{P} + Φ(σ_{P} ^{2}) where Φ is an arbitrary function. (For example, if Φ (x) = 3√x, the cost function is μ_{P} + 3σ_{P}.) To minimize uncertainty in the final result, it is meaningful to look for paths with bounded variance, i.e., σ_{P}^{2} ≤ B for a given fixed bound B. In this paper, we present an exact algorithm to solve the SSP problem in O(B(V + E)) time where V and E are the numbers of vertices and edges, respectively, in G. Our algorithm is superior to previous algorithms for SSP problem because we can handle: 1) general graphs (unlike previous works applicable only to directed acyclic graphs), 2) arbitrary edge-weight distributions (unlike previous algorithms designed only for specific distributions such as Gaussian), and 3) general cost function (none of the previous algorithms can even handle the cost function μ_{P} + 3σ_{P}. Finally, we discuss applications of the SSP problem to maze routing, buffer insertions, and timing analysis under parameter variations.

Original language | English (US) |
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Title of host publication | Proceedings of the ASP-DAC 2006 |

Subtitle of host publication | Asia and South Pacific Design Automation Conference 2006 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 965-970 |

Number of pages | 6 |

ISBN (Print) | 0780394518, 9780780394513 |

DOIs | |

State | Published - 2006 |

Event | ASP-DAC 2006: Asia and South Pacific Design Automation Conference 2006 - Yokohama, Japan Duration: Jan 24 2006 → Jan 27 2006 |

### Publication series

Name | Proceedings of the Asia and South Pacific Design Automation Conference, ASP-DAC |
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Volume | 2006 |

### Other

Other | ASP-DAC 2006: Asia and South Pacific Design Automation Conference 2006 |
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Country/Territory | Japan |

City | Yokohama |

Period | 1/24/06 → 1/27/06 |

## ASJC Scopus subject areas

- Computer Science Applications
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering